Question

A study was conducted in which students were asked to estimate the number of calories in a cheeseburger. One group was asked to do this after thinking about a​ calorie-laden cheesecake. A second group was asked to do this after thinking about an organic fruit salad. The mean number of calories estimated was 772 for the group that thought about the cheesecake and 1046 for the group that thought about the organic fruit salad. Suppose that the study was based on a sample of 20 students in each​ group, and the standard deviation of the number of calories estimated was 128 for the people who thought about the cheesecake first and 144 for the people who thought about the organic fruit salad first.

The null and alternative hypotheses is

H0​: μ1≥μ2

H1​:μ1l<μ2

a. Assume the population variances are not equal. At the 0.10 level of​ significance, is there evidence that the mean estimated number of calories in the cheeseburger is lower for the people who thought about the cheesecake first than for the people who thought about the organic fruit salad​ first?

Find the test statistic:

tSTAT=

​p-value=

Answer 1

H0​: μ1≥μ2

H1​:μ1l<μ2

Sample 1 = Cheesecake

Sample 2 = Organic fruit

Here as the population variance is unknown we can use t test

SE
Sample N Mean StDev Mean
1 20 772 128 29
2 20 1046 144 32

Substitituting each values we get

t stat = -6.36

Difference = μ (1) - μ (2)
Estimate for difference: -274.0
90% upper bound for difference: -217.8
T-Test of difference = 0 (vs <): T-Value = -6.36 P-Value = 0.000 DF = 37

From t table for t value -6.36 and 37 DOF we get p value of 0.000

P is lowwer than significant level 0.1

therefore we reject null hypothesis and accept alternate hypothesis i.e μ1l<μ2