Question

Suppose we have data investigating test scores in four different school districts. We wish to test H0 : � = 30 vs. H1 : � ≠ 30 based on four samples of size 30. Determine which of the following samples would result in the smallest p-value? Sample 1: sample mean = 28; sample standard deviation S = 6 Sample 2: sample mean = 27; sample standard deviation S = 4 Sample 3: Sample mean = 32; sample standard deviation S = 2 Sample 4: Sample mean = 26; sample standard deviation S = 9

Answer 1

Given that, the null and the alternative hypotheses are,

1) Sample 1: sample mean = 28; sample standard deviation S = 6

Test statistic is,

2) Sample 2: sample mean = 27; sample standard deviation S = 4

Test statistic is,

3) Sample 3: Sample mean = 32; sample standard deviation S = 2

Test statistic is,

4) Sample 4: Sample mean = 26; sample standard deviation S = 9

Test statistic is,

Since, sample 3 has a highest test statistic value it has a smallest p-value.

Answer: sample 3