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Contingency table chi-square test | Probability and Statistics | Khan Academy

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Contingency Table Chi-Square Test
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{'title': 'Contingency table chi-square test | Probability and Statistics | Khan Academy', 'heatmap': [{'end': 329.211, 'start': 316.31, 'weight': 0.716}, {'end': 407.111, 'start': 347.702, 'weight': 0.742}], 'summary': 'A study on herbal flu prevention with 380 participants examines different treatments and their effects, resulting in a chi-squared statistic of 2.53, 2 degrees of freedom, and a conclusion that the null hypothesis cannot be rejected at a 10% significance level.', 'chapters': [{'end': 132.211, 'segs': [{'end': 27.017, 'src': 'embed', 'start': 0.691, 'weight': 0, 'content': [{'end': 6.272, 'text': "Let's say there are a couple of herbs that people believe help prevent the flu.", 'start': 0.691, 'duration': 5.581}, {'end': 12.494, 'text': 'So to test this, what we do is we wait for flu season and we randomly assign people to three different groups.', 'start': 6.432, 'duration': 6.062}, {'end': 19.715, 'text': 'And over the course of flu season, we have them either in one group taking herb one and the second group taking herb two.', 'start': 12.894, 'duration': 6.821}, {'end': 21.836, 'text': 'And in the third group, they take a placebo.', 'start': 20.056, 'duration': 1.78}, {'end': 27.017, 'text': "And if you don't know what a placebo is, it's something that to the patient or to the person participating,", 'start': 21.856, 'duration': 5.161}], 'summary': 'To test flu prevention, people are assigned to groups taking different herbs and a placebo during flu season.', 'duration': 26.326, 'max_score': 0.691, 'thumbnail': 'https://coursnap.oss-ap-southeast-1.aliyuncs.com/video-capture/hpWdDmgsIRE/pics/hpWdDmgsIRE691.jpg'}, {'end': 82.047, 'src': 'embed', 'start': 51.531, 'weight': 1, 'content': [{'end': 57.215, 'text': "And a very small amount of sugar, so it really can't affect their actual likelihood of getting the flu.", 'start': 51.531, 'duration': 5.684}, {'end': 60.687, 'text': 'So over here, we have a table.', 'start': 58.186, 'duration': 2.501}, {'end': 67.83, 'text': 'And this is actually called a contingency table.', 'start': 60.727, 'duration': 7.103}, {'end': 73.772, 'text': "And it has on it, in each group, the number that got sick, the number that didn't get sick.", 'start': 68.95, 'duration': 4.822}, {'end': 76.854, 'text': 'And so we also can, from this, calculate the total number.', 'start': 74.193, 'duration': 2.661}, {'end': 82.047, 'text': 'In group one, we had a total of 120 people.', 'start': 78.442, 'duration': 3.605}], 'summary': "A small amount of sugar can't affect flu likelihood. group one had 120 people.", 'duration': 30.516, 'max_score': 51.531, 'thumbnail': 'https://coursnap.oss-ap-southeast-1.aliyuncs.com/video-capture/hpWdDmgsIRE/pics/hpWdDmgsIRE51531.jpg'}, {'end': 134.792, 'src': 'embed', 'start': 105.826, 'weight': 2, 'content': [{'end': 108.907, 'text': "And then the total people that didn't get sick over here is 100 plus 110 is 210, plus 90 is 300.", 'start': 105.826, 'duration': 3.081}, {'end': 109.827, 'text': 'And then the total people here are 380.', 'start': 108.907, 'duration': 0.92}, {'end': 122.947, 'text': 'Both this column and this row should add up to 380.', 'start': 109.827, 'duration': 13.12}, {'end': 123.907, 'text': 'So, with that out of the way,', 'start': 122.947, 'duration': 0.96}, {'end': 132.211, 'text': "let's think about how we can use this information in the contingency table and our knowledge of the chi-squared distribution to come up with some conclusion.", 'start': 123.907, 'duration': 8.304}, {'end': 134.792, 'text': "So let's just make a null hypothesis.", 'start': 132.792, 'duration': 2}], 'summary': "210 people didn't get sick out of 380. using chi-squared distribution for conclusion.", 'duration': 28.966, 'max_score': 105.826, 'thumbnail': 'https://coursnap.oss-ap-southeast-1.aliyuncs.com/video-capture/hpWdDmgsIRE/pics/hpWdDmgsIRE105826.jpg'}], 'start': 0.691, 'title': 'Herbal flu prevention study', 'summary': 'Discusses a study on herbal flu prevention with 380 participants, examining different treatments and their effects on flu prevention during the flu season.', 'chapters': [{'end': 132.211, 'start': 0.691, 'title': 'Herbal flu prevention study', 'summary': 'Discusses a study on herbal flu prevention, where three groups were assigned to take different treatments during flu season, resulting in a contingency table with the total number of people and the number of sick and healthy individuals in each group, totaling 380 participants.', 'duration': 131.52, 'highlights': ['Three groups were assigned to take different treatments during flu season', 'Contingency table with the total number of people and the number of sick and healthy individuals in each group', 'Totaling 380 participants']}], 'duration': 131.52, 'thumbnail': 'https://coursnap.oss-ap-southeast-1.aliyuncs.com/video-capture/hpWdDmgsIRE/pics/hpWdDmgsIRE691.jpg', 'highlights': ['Three groups were assigned to take different treatments during flu season', 'Contingency table with the total number of people and the number of sick and healthy individuals in each group', 'Totaling 380 participants']}, {'end': 754.147, 'segs': [{'end': 163.045, 'src': 'embed', 'start': 132.792, 'weight': 1, 'content': [{'end': 134.792, 'text': "So let's just make a null hypothesis.", 'start': 132.792, 'duration': 2}, {'end': 137.194, 'text': 'Our null hypothesis is that the herbs do nothing.', 'start': 134.832, 'duration': 2.362}, {'end': 138.974, 'text': 'Let me get some space here.', 'start': 137.214, 'duration': 1.76}, {'end': 143.096, 'text': "So let's assume the null hypothesis that the herbs do nothing.", 'start': 139.254, 'duration': 3.842}, {'end': 156.283, 'text': 'And then we have our alternative hypothesis, our alternate hypothesis, that the herbs do something.', 'start': 151.721, 'duration': 4.562}, {'end': 161.685, 'text': "Notice, I don't even care whether they actually improve.", 'start': 156.303, 'duration': 5.382}, {'end': 163.045, 'text': "I'm just saying they do something.", 'start': 161.725, 'duration': 1.32}], 'summary': 'Null hypothesis: herbs have no effect. alternate hypothesis: herbs have some effect.', 'duration': 30.253, 'max_score': 132.792, 'thumbnail': 'https://coursnap.oss-ap-southeast-1.aliyuncs.com/video-capture/hpWdDmgsIRE/pics/hpWdDmgsIRE132792.jpg'}, {'end': 214.74, 'src': 'embed', 'start': 188.022, 'weight': 0, 'content': [{'end': 191.564, 'text': 'And if it is really low, then we will reject the null hypothesis.', 'start': 188.022, 'duration': 3.542}, {'end': 195.265, 'text': 'And in this test, like every hypothesis test, we need a significance level.', 'start': 191.964, 'duration': 3.301}, {'end': 200.087, 'text': "And let's say our significance level we care about, for whatever reason, is 10%, or 0.10, or 10%.", 'start': 195.625, 'duration': 4.462}, {'end': 203.829, 'text': "That's the significance level that we care about.", 'start': 200.087, 'duration': 3.742}, {'end': 214.74, 'text': 'Now, to do this, we have to calculate a chi-square statistic for this contingency table.', 'start': 207.839, 'duration': 6.901}], 'summary': 'Using a 10% significance level, a chi-square statistic is calculated for a contingency table.', 'duration': 26.718, 'max_score': 188.022, 'thumbnail': 'https://coursnap.oss-ap-southeast-1.aliyuncs.com/video-capture/hpWdDmgsIRE/pics/hpWdDmgsIRE188022.jpg'}, {'end': 347.702, 'src': 'heatmap', 'start': 316.31, 'weight': 0.716, 'content': [{'end': 317.611, 'text': '21% did not get sick.', 'start': 316.31, 'duration': 1.301}, {'end': 318.872, 'text': 'So let me write that over here.', 'start': 317.631, 'duration': 1.241}, {'end': 326.87, 'text': 'So 21%.', 'start': 318.892, 'duration': 7.978}, {'end': 327.37, 'text': "That's 21% of the total.", 'start': 326.87, 'duration': 0.5}, {'end': 329.211, 'text': 'And then this would be 79% if we just subtract 1 minus 21.', 'start': 327.41, 'duration': 1.801}, {'end': 330.131, 'text': 'We could divide 300 by 380.', 'start': 329.211, 'duration': 0.92}, {'end': 331.412, 'text': 'We should get 79% as well.', 'start': 330.131, 'duration': 1.281}, {'end': 347.702, 'text': 'So one would expect that 21% of each of your total, based on the total sample right over here that you Our best guess,', 'start': 331.452, 'duration': 16.25}], 'summary': '21% did not get sick, 79% did, based on sample.', 'duration': 31.392, 'max_score': 316.31, 'thumbnail': 'https://coursnap.oss-ap-southeast-1.aliyuncs.com/video-capture/hpWdDmgsIRE/pics/hpWdDmgsIRE316310.jpg'}, {'end': 407.111, 'src': 'heatmap', 'start': 347.702, 'weight': 0.742, 'content': [{'end': 351.965, 'text': 'is that 21% should be getting sick and 79% should not be getting sick.', 'start': 347.702, 'duration': 4.263}, {'end': 354.287, 'text': "So let's look at it for each of these groups.", 'start': 352.466, 'duration': 1.821}, {'end': 362.553, 'text': 'If we assume that 21% of these 120 people should have gotten sick, what would have been the expected value right over here?', 'start': 354.687, 'duration': 7.866}, {'end': 363.554, 'text': "So let's just multiply 21%.", 'start': 362.573, 'duration': 0.981}, {'end': 364.514, 'text': "Let's just multiply this 21% times 120.", 'start': 363.554, 'duration': 0.96}, {'end': 366.396, 'text': "So let's just multiply that times 120.", 'start': 364.514, 'duration': 1.882}, {'end': 374.588, 'text': 'That gets us to 25.2.', 'start': 366.396, 'duration': 8.192}, {'end': 376.109, 'text': "I'll just round it.", 'start': 374.588, 'duration': 1.521}, {'end': 378.49, 'text': '25.3 people should have gotten sick.', 'start': 376.129, 'duration': 2.361}, {'end': 381.192, 'text': 'So the expected, so let me write it over here.', 'start': 378.51, 'duration': 2.682}, {'end': 383.814, 'text': "I'll do expected in yellow.", 'start': 381.212, 'duration': 2.602}, {'end': 392.039, 'text': 'So the expected right over here, if you assume the 21% of each group should have gotten sick,', 'start': 384.474, 'duration': 7.565}, {'end': 398.903, 'text': 'is that you would have expected 25.3 people to get sick in group one in herb one group.', 'start': 392.039, 'duration': 6.864}, {'end': 407.111, 'text': "And then the remainder will not get sick, so let's just subtract Let's just, or I could actually multiply 79% times 120.", 'start': 399.263, 'duration': 7.848}], 'summary': 'Expected 25.3 people to get sick out of 120, with 79% not getting sick.', 'duration': 59.409, 'max_score': 347.702, 'thumbnail': 'https://coursnap.oss-ap-southeast-1.aliyuncs.com/video-capture/hpWdDmgsIRE/pics/hpWdDmgsIRE347702.jpg'}, {'end': 475.949, 'src': 'embed', 'start': 446.404, 'weight': 3, 'content': [{'end': 451.085, 'text': "And then the remainder, let's see, 140 minus 29.4, should not have gotten sick.", 'start': 446.404, 'duration': 4.681}, {'end': 453.546, 'text': 'So that gets us this right here.', 'start': 451.125, 'duration': 2.421}, {'end': 457.224, 'text': 'We have 20.', 'start': 454.566, 'duration': 2.658}, {'end': 460.945, 'text': '29.4 should have gotten sick if the herbs did nothing.', 'start': 457.224, 'duration': 3.721}, {'end': 468.768, 'text': 'And then over here, we would have 110.6 should not have gotten sick.', 'start': 461.405, 'duration': 7.363}, {'end': 470.108, 'text': 'And these are pretty close.', 'start': 469.168, 'duration': 0.94}, {'end': 475.949, 'text': "So just looking at the numbers, it looks like this herb doesn't do too much relative to all of the groups combined.", 'start': 470.128, 'duration': 5.821}], 'summary': "Out of 140, 29.4 should have gotten sick, but only 20 did, indicating the herbs' potential effectiveness.", 'duration': 29.545, 'max_score': 446.404, 'thumbnail': 'https://coursnap.oss-ap-southeast-1.aliyuncs.com/video-capture/hpWdDmgsIRE/pics/hpWdDmgsIRE446404.jpg'}, {'end': 614.309, 'src': 'embed', 'start': 571.452, 'weight': 2, 'content': [{'end': 576.115, 'text': 'Actually, let me write it the curly X, just so you see that some people write it with the chi instead of the X.', 'start': 571.452, 'duration': 4.663}, {'end': 578.057, 'text': 'So our chi-square statistic over here.', 'start': 576.115, 'duration': 1.942}, {'end': 586.054, 'text': "We're literally just going to find the squared distance between the observed and expected and then divide it by the expected.", 'start': 578.931, 'duration': 7.123}, {'end': 588.755, 'text': "So it's going to be 20 minus 25.3 squared over 25.3 plus 30 minus 29.4 squared over 29.4.", 'start': 586.074, 'duration': 2.681}, {'end': 590.616, 'text': "I'm going to run out of space.", 'start': 588.755, 'duration': 1.861}, {'end': 614.309, 'text': '30 minus 25.3 squared over 25.3.', 'start': 609.545, 'duration': 4.764}], 'summary': 'Explaining chi-square calculation with specific values and formula', 'duration': 42.857, 'max_score': 571.452, 'thumbnail': 'https://coursnap.oss-ap-southeast-1.aliyuncs.com/video-capture/hpWdDmgsIRE/pics/hpWdDmgsIRE571452.jpg'}], 'start': 132.792, 'title': 'Hypothesis testing and chi-squared statistic', 'summary': 'Discusses hypothesis testing with herbs and chi-squared statistic calculation, illustrating the significance level and chi-square statistic calculation for a contingency table, and resulting in a chi-squared statistic of 2.53.', 'chapters': [{'end': 256.559, 'start': 132.792, 'title': 'Hypothesis testing with herbs', 'summary': 'Discusses hypothesis testing using a null hypothesis that the herbs do nothing and an alternative hypothesis that the herbs do something, illustrating the significance level and chi-square statistic calculation for a contingency table.', 'duration': 123.767, 'highlights': ['The chapter explains the concept of null and alternative hypotheses in the context of testing the effect of herbs, emphasizing that the focus is on determining whether the herbs have any effect, not necessarily a positive one.', 'It discusses the process of assuming the null hypothesis and calculating the likelihood of obtaining data as extreme as the observed, and the subsequent rejection of the null hypothesis if the likelihood is very low, with a specified significance level of 10%.', 'The significance level of 10% is identified as a key aspect in the hypothesis testing process, indicating the threshold for rejecting the null hypothesis based on the calculated chi-square statistic for the contingency table.']}, {'end': 754.147, 'start': 256.559, 'title': 'Chi-squared statistic calculation', 'summary': 'Explains how to calculate the chi-squared statistic for a sample data set to assess the significance of the observed versus expected values, resulting in a chi-squared statistic of 2.53.', 'duration': 497.588, 'highlights': ['The expected frequency of getting sick and not getting sick is calculated based on the assumption that the herbs have no effect, with an expected 21% getting sick and 79% not getting sick from the total sample of 380, leading to an expected 25.3 people getting sick in one group and 94.7 not getting sick.', "An analysis of multiple groups suggests that the herb's impact is minimal, as the expected and observed values show no substantial differences, with the chi-squared statistic calculated as 2.53 to assess the significance of the differences.", 'The detailed methodology for calculating the chi-squared statistic involves finding the squared difference between observed and expected values for each group and dividing it by the expected value, resulting in the final chi-squared statistic of 2.53.']}], 'duration': 621.355, 'thumbnail': 'https://coursnap.oss-ap-southeast-1.aliyuncs.com/video-capture/hpWdDmgsIRE/pics/hpWdDmgsIRE132792.jpg', 'highlights': ['The significance level of 10% is a key aspect in the hypothesis testing process, indicating the threshold for rejecting the null hypothesis based on the calculated chi-square statistic for the contingency table.', 'The chapter explains the concept of null and alternative hypotheses in the context of testing the effect of herbs, emphasizing that the focus is on determining whether the herbs have any effect, not necessarily a positive one.', 'The detailed methodology for calculating the chi-squared statistic involves finding the squared difference between observed and expected values for each group and dividing it by the expected value, resulting in the final chi-squared statistic of 2.53.', "An analysis of multiple groups suggests that the herb's impact is minimal, as the expected and observed values show no substantial differences, with the chi-squared statistic calculated as 2.53 to assess the significance of the differences."]}, {'end': 1055.685, 'segs': [{'end': 833.054, 'src': 'embed', 'start': 754.147, 'weight': 1, 'content': [{'end': 771.901, 'text': 'So our chi-square statistic, assuming the null hypothesis is correct, is equal to 2.53.', 'start': 754.147, 'duration': 17.754}, {'end': 777.966, 'text': 'Now, the next thing we have to do is figure out the degrees of freedom that we had in calculating this chi-square statistic.', 'start': 771.901, 'duration': 6.065}, {'end': 783.691, 'text': "And I'll give you the rule of thumb, and I'll give you a little bit of a sense of why this is the rule of thumb for a contingency table like this.", 'start': 778.286, 'duration': 5.405}, {'end': 787.573, 'text': "And in the future, we'll talk a little bit more deeply about degrees of freedom.", 'start': 784.15, 'duration': 3.423}, {'end': 792.338, 'text': 'So the rule of thumb for a contingency table is you have the number of rows.', 'start': 788.414, 'duration': 3.924}, {'end': 795.641, 'text': 'So you have rows and then you have your number of columns.', 'start': 792.798, 'duration': 2.843}, {'end': 798.084, 'text': 'So here we have two rows and we have three columns.', 'start': 796.022, 'duration': 2.062}, {'end': 799.105, 'text': "You don't count the totals.", 'start': 798.104, 'duration': 1.001}, {'end': 801.187, 'text': 'So you have three columns over here.', 'start': 799.605, 'duration': 1.582}, {'end': 804.45, 'text': 'And the degrees of freedom, and this is the rule of thumb.', 'start': 801.727, 'duration': 2.723}, {'end': 815.465, 'text': 'The degrees of freedom for your contingency table is going to be the number of rows minus 1 times the number of columns minus 1.', 'start': 807.421, 'duration': 8.044}, {'end': 819.287, 'text': 'In our situation, we have two rows and three columns.', 'start': 815.465, 'duration': 3.822}, {'end': 823.569, 'text': "So it's going to be 2 minus 1 times 3 minus 1.", 'start': 819.667, 'duration': 3.902}, {'end': 831.433, 'text': "So it's going to be 2 minus 1 times 3 minus 1, which is just 1 times 2, which is 2.", 'start': 823.569, 'duration': 7.864}, {'end': 833.054, 'text': 'We have two degrees of freedom.', 'start': 831.433, 'duration': 1.621}], 'summary': 'Chi-square statistic is 2.53 with 2 degrees of freedom.', 'duration': 78.907, 'max_score': 754.147, 'thumbnail': 'https://coursnap.oss-ap-southeast-1.aliyuncs.com/video-capture/hpWdDmgsIRE/pics/hpWdDmgsIRE754147.jpg'}, {'end': 990.709, 'src': 'embed', 'start': 933.149, 'weight': 0, 'content': [{'end': 940.216, 'text': 'So what we need to do is to figure out, with a chi-square distribution and two degrees of freedom, what is our critical chi-square statistic?', 'start': 933.149, 'duration': 7.067}, {'end': 941.257, 'text': "So let's just go back.", 'start': 940.296, 'duration': 0.961}, {'end': 944.88, 'text': 'So we have two degrees of freedom here.', 'start': 942.017, 'duration': 2.863}, {'end': 947.582, 'text': 'And we care about a significance level of 10%.', 'start': 944.96, 'duration': 2.622}, {'end': 959.081, 'text': 'So our critical chi-square value is 4.60.', 'start': 947.582, 'duration': 11.499}, {'end': 962.423, 'text': 'So another way to visualize this.', 'start': 959.081, 'duration': 3.342}, {'end': 965.605, 'text': 'if we look at the chi-square distribution with two degrees of freedom,', 'start': 962.423, 'duration': 3.182}, {'end': 975.39, 'text': "that's this blue one over here at a value of I'm trying to pick a nice blue to use at a value of a critical value of 4.60, so 4.60, this is 5,", 'start': 965.605, 'duration': 9.785}, {'end': 986.786, 'text': 'so 4.60 will be right around here at a critical value of 4.60, so this is 4.60,.', 'start': 975.39, 'duration': 11.396}, {'end': 990.709, 'text': 'You have the probability of getting something at least that extreme.', 'start': 986.786, 'duration': 3.923}], 'summary': 'Using chi-square distribution with 2 degrees of freedom, the critical chi-square value at a 10% significance level is 4.60.', 'duration': 57.56, 'max_score': 933.149, 'thumbnail': 'https://coursnap.oss-ap-southeast-1.aliyuncs.com/video-capture/hpWdDmgsIRE/pics/hpWdDmgsIRE933149.jpg'}], 'start': 754.147, 'title': 'Chi-square statistic and degrees of freedom', 'summary': 'Discusses chi-square statistic of 2.53, 2 degrees of freedom, and uses a significance level of 10% to determine the critical chi-square value, leading to the conclusion that the null hypothesis cannot be rejected.', 'chapters': [{'end': 833.054, 'start': 754.147, 'title': 'Chi-square statistic and degrees of freedom', 'summary': 'Discusses the chi-square statistic of 2.53 assuming the null hypothesis is correct and explains the calculation of degrees of freedom for a contingency table with 2 rows and 3 columns, resulting in 2 degrees of freedom.', 'duration': 78.907, 'highlights': ['The chi-square statistic is 2.53 assuming the null hypothesis is correct, providing a quantifiable value for the statistical test.', 'The rule of thumb for calculating degrees of freedom for a contingency table is to multiply the number of rows minus 1 by the number of columns minus 1, resulting in 2 degrees of freedom for the given 2 rows and 3 columns.', 'The explanation of degrees of freedom for a contingency table is provided, laying the foundation for a deeper understanding of the concept in future discussions.']}, {'end': 1055.685, 'start': 834.005, 'title': 'Chi-square test and degrees of freedom', 'summary': 'Discusses the concept of degrees of freedom and uses the chi-square statistic with 2 degrees of freedom and a significance level of 10% to determine the critical chi-square value, leading to the conclusion that the null hypothesis cannot be rejected based on the data.', 'duration': 221.68, 'highlights': ['The chi-square statistic has two degrees of freedom and a significance level of 10%.', 'The critical chi-square value is determined to be 4.60.', 'The calculated chi-square statistic is only 2.53, leading to the inability to reject the null hypothesis based on the data.']}], 'duration': 301.538, 'thumbnail': 'https://coursnap.oss-ap-southeast-1.aliyuncs.com/video-capture/hpWdDmgsIRE/pics/hpWdDmgsIRE754147.jpg', 'highlights': ['The critical chi-square value is determined to be 4.60', 'The chi-square statistic is 2.53 assuming the null hypothesis is correct', 'The chi-square statistic has two degrees of freedom and a significance level of 10%', 'The rule of thumb for calculating degrees of freedom for a contingency table is to multiply the number of rows minus 1 by the number of columns minus 1, resulting in 2 degrees of freedom', 'The explanation of degrees of freedom for a contingency table is provided, laying the foundation for a deeper understanding of the concept in future discussions']}], 'highlights': ['Contingency table with the total number of people and the number of sick and healthy individuals in each group', 'Totaling 380 participants', 'The detailed methodology for calculating the chi-squared statistic involves finding the squared difference between observed and expected values for each group and dividing it by the expected value, resulting in the final chi-squared statistic of 2.53', 'The chi-square statistic has two degrees of freedom and a significance level of 10%', 'The critical chi-square value is determined to be 4.60', 'The rule of thumb for calculating degrees of freedom for a contingency table is to multiply the number of rows minus 1 by the number of columns minus 1, resulting in 2 degrees of freedom', "An analysis of multiple groups suggests that the herb's impact is minimal, as the expected and observed values show no substantial differences, with the chi-squared statistic calculated as 2.53 to assess the significance of the differences", 'The significance level of 10% is a key aspect in the hypothesis testing process, indicating the threshold for rejecting the null hypothesis based on the calculated chi-square statistic for the contingency table', 'The chapter explains the concept of null and alternative hypotheses in the context of testing the effect of herbs, emphasizing that the focus is on determining whether the herbs have any effect, not necessarily a positive one', 'The chi-square statistic is 2.53 assuming the null hypothesis is correct', 'Three groups were assigned to take different treatments during flu season']}