A student recorded the number of calories in samples of vegetarian and nonvegetarian entrees served by a college dining hall. The student wanted to conduct a hypothesis test of whether the sample data provide evidence that the population mean calorie amounts differ between these two groups.
Summary statistics of the data are provided in the following table: The two-sample $t$-test statistic turns out to equal 0.92 .
a. State the appropriate null and alternative hypotheses in symbols.
b. Do you have enough information to check the technical conditions for a two-sample $t$-test? Explain.
c. Determine the $p$-value as accurately as possible. (Explain what table you use and how you use it.)
d. Summarize your conclusion in a sentence or two, as if you were the statistical consultant reporting back to the student who conducted the study.
e. Describe how the $p$-value would change (smaller, larger, or no change) if all else were the same except the following. (No explanations are needed.)
The sample standard deviations were larger.
The sample sizes were larger.
The sample means were further apart.

Question

A student recorded the number of calories in samples of vegetarian and nonvegetarian entrees served by a college dining hall. The student wanted to conduct a hypothesis test of whether the sample data provide evidence that the population mean calorie amounts differ between these two groups.
Summary statistics of the data are provided in the following table:  The two-sample $t$-test statistic turns out to equal 0.92 .
a. State the appropriate null and alternative hypotheses in symbols.
b. Do you have enough information to check the technical conditions for a two-sample $t$-test? Explain.
c. Determine the $p$-value as accurately as possible. (Explain what table you use and how you use it.)
d. Summarize your conclusion in a sentence or two, as if you were the statistical consultant reporting back to the student who conducted the study.
e. Describe how the $p$-value would change (smaller, larger, or no change) if all else were the same except the following. (No explanations are needed.)
The sample standard deviations were larger.
The sample sizes were larger.
The sample means were further apart.

Quizplus · Accepted Answer

The Answer of A student recorded the number of calories in samples of vegetarian and nonvegetarian entrees served by a college dining hall. The student wanted to conduct a hypothesis test of whether the sample data provide evidence that the population mean calorie amounts differ between these two groups.
Summary statistics of the data are provided in the following table:  The two-sample $t$-test statistic turns out to equal 0.92 .
a. State the appropriate null and alternative hypotheses in symbols.
b. Do you have enough information to check the technical conditions for a two-sample $t$-test? Explain.
c. Determine the $p$-value as accurately as possible. (Explain what table you use and how you use it.)
d. Summarize your conclusion in a sentence or two, as if you were the statistical consultant reporting back to the student who conducted the study.
e. Describe how the $p$-value would change (smaller, larger, or no change) if all else were the same except the following. (No explanations are needed.)
The sample standard deviations were larger.
The sample sizes were larger.
The sample means were further apart.

A Student Recorded the Number of Calories in Samples of Vegetarian