Chapter 10: Q. 52. (page 668)

Ice cream For a statistics class project, Jonathan and Crystal held an ice-cream-eating contest. They randomly selected 29 males and 35 females from their large high school to participate. Each student was given a small cup of ice cream and instructed to eat it as fast as possible. Jonathan and Crystal then recorded each contestant’s gender and time (in seconds), as shown in the dot plots.
Do these data give convincing evidence of a difference in the population means at the α=0.10 $\frac{305}{1526} = 0.200 = 20.0 % α = 0.10$ significance level?
a. State appropriate hypotheses for performing a significance test. Be sure to define the parameters of interest.
b. Check if the conditions for performing the test are met.

Short Answer

Expert verified

Part a) The hypothesis is:

$H_{0} : μ_{1} = μ_{2} H_{0} : μ_{1} n o t e q u a l t o μ_{2}$

Part b) All conditions are not met.

Step by step solution

Part a) Step 1: Given information

The given claim is that a difference in the means.

Part b) Step 2: Explanation

We must now determine the appropriate hypotheses for performing a significance test.

As a result, the claim represents either the null hypothesis or the alternative hypothesis. According to the null hypothesis, the population proportions are equal. If the claim is the null hypothesis, then the alternative hypothesis states the inverse of the null hypothesis.

Therefore, the following are the appropriate hypotheses:

$H_{0} : μ_{1} = μ_{2} H_{a} : μ_{1} n o t e q u a l t o μ_{2}$

$μ_{1} =$ the true mean time for males to eat ice cream.

$μ_{2} =$ the true mean time for females to eat ice cream.

Part b) Step 1: Explanation

There are three requirements that must be met:

It is satisfying because the samples are drawn at random from different populations.

Independent: It is satisfying because the sample of $29$ male students represents less than $10 %$ of the total population of male students, and the sample of $35$ female students represents less than $10 %$ of the total population of female students.

Normal: It is not satisfactory because the sample size for male students is small and the male distribution is not approximately Normal, as shown by the skewed pattern in the dot plot.

Therefore, all the conditions are not satisfied since the large sample condition is not satisfied and it is then not appropriate to perform a hypothesis test for the mean difference.