Question

Suppose that Max is a climate change scientist and butterfly enthusiast. In Max's locale, the mean summer temperature over the last ten years was higher than it was in the previous ten years. Max wonders if the size of adult male monarch butterflies has changed with the temperature difference. He knows that in his locale, historically, the mean rear wing length of adult male monarchs was 38.3 mm. He collects a random sample of n adult male monarchs to compare to the historical average. His sample data is shown in the given stem-and-leaf plot, where the stem unit is mm and the leaf unit is tenths of a mm. 35 1 2 36 5 6 7 8 37 0 38 0 5 6 1 2 3 8 2 4 4 8 9 39 3 5 Leaf unit 0.1 mm From experience, Max knows that the rear wing length of monarch butterflies is normally distributed. He decides to use a t- test with a significance level of a = 0.05 to test the null hypothesis, Ho : u = 38.3 against the alternative hypothesis, 38.3, where u is the population mean. H1 If the requirements for a t-test have not been met, only state the test decision and conclusion. Otherwise, find the mean, standard deviation, t-statistic, P-value, and state the test decision and conclusion. First, compute the mean, x, of Max's sample. Report your answer with two decimals of precision.

Answer 1

Sal Hoi l = 38.3 H: 1 € 38.3 &=0.05 te sum of all observations total no. of observations t = 787.9 37.52 21 5 = so n-1 S= 27.87238 27.87238 20 S= 1.18 Test - statistic, t= - ll slun

t = 37.52 - 38.3 101815 t – – 3.029 . p-value = 0.007 since, p-value ca. so, we reject null hypothesis Max should make the decision to reject the well my pathesis. The conclusion is that there is sufficient evidence that the current mean wing size adult mall monarch butterflies is different of than 38.3 mm.