Question

he mean age of graduate students at a University is thought to
be 31 years old.

A random sample of 15 graduate students is taken. The sample mean
age is 33 years and the sample standard deviation is three
years.

Does the sample data indicate that the population mean age is
actually greater than 31 years old? Use a 1% level of
significance.

**a.)** What is α? State the null and alternate
hypotheses. Will you use a left-tailed, right-tailed, or two-tailed
test?

αα =

H0H0: μμ =

H1H1: μμ Select an answer > < not =

The test is a Select an answer two-tailed right-tailed
left-tailed test

**b.)** Identify the Sampling Distribution you will
use. What is the value of the test statistic?

The best sampling distribution to use is the Select an answer
Normal Student's t distribution.

The test statistic (z or t value) is =

**c.)** Find or estimate the P-value for the
test.

The p-value is = Select an answer Between 0.025 and 0.050 Between
0.100 and 0.125 Between 0.075 and 0.100 Between 0.050 and 0.075
Between 0.010 and 0.025

**d.)** Conclude the test.

Based on this we will Select an answer Reject Fail to
reject the null hypothesis.

LicensePoints possible: 16

Answer #1

This is the right tailed test .

The null and alternative hypothesis is

H_{0} : = 31

H_{a} :
> 31

Test statistic = t

= ( - ) / s / n

= (33 - 31) / 3 / 15

**Test statistic = 2.582**

df = 15 - 1 = 14

**Between 0.010 and 0.025**

P-value >

**Fail to reject the null hypothesis .**

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