Question

The Federal Pell Grant Program gives grants to low-income undergraduate students. According to the National Postsecondary Student Aid Study conducted by the U.S. Department of Education in 2008, the average Pell grant award for 2007-2008 was $2,600.

We wonder if the mean amount is different this year for Pell grant recipients at San Jose State University. Suppose that we randomly select 50 Pell grant recipients from San Jose State University. For these 50 students, the mean Pell grant award is $2,450 with a standard deviation of $600.

Let $LaTeX: \mu$ μ = the mean amount of Pell grant awards received by San Jose State University Pell grant recipients this year. We test the following hypotheses.

H 0: $LaTeX: \mu=2600$ μ = 2600

H a: $LaTeX: \mu\ne2600$ μ ≠ 2600

The sample size is greater than 30, so a t-model is a good fit for the sampling distribution.

Use this information to answer the next two questions.

1.What is the t-test statistic? If necessary, round to two decimal places.

2.What is the P-value? If necessary, round to three decimal places.

3.Suppose a quantitative variable is normally distributed in the population. We conduct a t-test for a population mean with the following hypotheses.

H 0: $LaTeX: \mu=50$ μ = 50

H a: $LaTeX: \mu\ne50$ μ ≠ 50

A sample of size 30 has a t-statistic of − 2.43. Find the corresponding P-value. Do not round.

4.For a quantitative variable that is normally distributed in the population, suppose that we test the hypotheses

H 0: $LaTeX: \mu=50$ μ = 50

H a: $LaTeX: \mu>50$ μ > 50

Further suppose that a sample of size 30 has a t-statistic of 2.43. Find the corresponding P-value. (See if you can figure this out without using the applet. Give it a try!)

Group of answer choices

0.0108

0.0216

0.9892

Answer 1

1)

Test statistic,
t = (xbar - mu)/(s/sqrt(n))
t = (2450 - 2600)/(600/sqrt(50))
t = -1.77

2)

P-value Approach
P-value = 0.083

3)

p value =0.0216

4)

0.0216