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 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: μ = 2600 H a: 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. Flag this Question Question 12.5 pts What is the t-test statistic? If necessary, round to two decimal places.

Answer 1

Answer: the t-test statistic is - 1.77

Step-by-step explanation:

For the null hypothesis,

H 0: μ = 2600

For the alternative hypothesis,

H a: μ ≠ 2600

This is a two tailed test

Since no population standard deviation is given, the distribution is a student's t.

Since n = 50,

Degrees of freedom, df = n - 1 = 50 - 1 = 49

t = (x - µ)/(s/√n)

Where

x = sample mean = $2450

µ = population mean = $2600

s = samples standard deviation = $600

Therefore,

t = (2450 - 2600)/(600/√50) = - 1.77