Question

Use the following information for the next two problems. A college student is on a “meal program.” His budget allows him to spend an average of $10 per day for the semester. He randomly selects 14 days from the semester and finds his mean daily expense, for those days, to be $14.09 with a sample standard deviation of $8.05. Assume that the observations come from a normal distribution.

1.Which one of the following gives the null and alternative hypotheses to test if the college student overspent his food allowance?

	a.
	b.
	c.
	d.

b. Calculate the test statistic.

Answer 1

1)

A college student is on a "meal program". His budget allows him to spend an average of $10 per day for the semester.

Here, we need to find null hypothesis and alternative hypothesis if the college student overspent his food allowance.

The hypotheses are given by

The null hypothesis

The alternative hypothesis

2)

Here, we need to find the value of test statistic.

He randomly selects 14 days from the semester and finds his mean daily expense, for those days, to be $14.09 with a sample standard deviation of $8.05. Assume that the observations come from a normal distribution.

Here, observation are comes from normal distribution, but population standard deviation is not know.

So, we will use here t-distribution

The test statistic is

Here the values are given by

The value of test statistic is 1.90