A second researcher wishes to determine if Hendrix students eat more M&Ms on average than all college students. This person establishes a significance level of α = 0.05 and creates a sample of size 28. They determine a p value of 0.08, which is ever so slightly above α. Disappointed, they then choose a new sample, of size 25, and determine p = 0.23. They do this five more times (for a total of 7 samples), with various sizes between 25 and 30. Their p values are 0.15, 0.32, 0.09, 0.16, and 0.02. Their final sample gave a p value smaller than the significance level and since this should happen by chance only once in 20 samples, they reason that they have found a real difference, since it only took them 7 tries, and therefore claim that Hendrix students do in fact eat more M&Ms than the average college student does. What can you say about their result and methodology?

Suppose IQ scores were obtained for 20 randomly selected sets of siblings. The 20 pairs of measurements yield x=103.36​, y=103.45​, r=0.928​, ​P-value= 0.000, and y=−7.2+1.07x​,where x represents the IQ score of the older child.Find the best predicted value of y given that the older child has an IQ of 106? Use a significance level of 0.05

Suppose IQ scores were obtained for 20 randomly selected sets of couples. The 20 pairs of measurements yield x=102.2​, y=100.8​, r=0.854​, ​P-value=​0.000, and y=24.13+0.75x​, where x represents the IQ score of the wife. Find the best predicted value of y given that the wife has an IQ of 95​? Use a significance level of 0.05.   LOADING... Click the icon to view the critical values of the Pearson correlation coefficient r. The best predicted value of y is nothing.

1. Birds can regrow feathers if they are lost. A researcher was interested in whether newly regrown feathers in the tails of northern flickers differed in colour (yellowness in particular) compared to older feathers. To test this, they measured the yellowness of one new and one randomly selected old feather on each of 20 birds. A plot of their data and the results of their analysis are shown below. Yellowness 160 150 140 130 new X Feather old Welch Two Sample t-test = data: Yellowness by Feather t = 1.5832, df 37.986, p-value 165 sample estimates: mean in group new mean in group old 147.9623 143.3000 160 New 155 150 145 140 135 = 0.1217 alternative hypothesis: true difference in means is not equal to 0 95 percent confidence interval: -1.299296 10.623962 T T T T T 130 135 140 145 150 155 160 Old a) From the results above, what is the null hypothesis and what statistical conclusion do you make concerning it?