Question

Asked Nov 20, 2019

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Test the claim that the mean GPA of night students is significantly different than 2.7 at the 0.02 significance level.

Based on a sample of 80 people, the sample mean GPA was 2.74 with a standard deviation of 0.05

The test statistic is:

The positive critical value is:

how do you do this on a ti 84

I tried the t test but it says it is not right

Step 1

It is given that sample mean and standard deviation are 2.74 and 0.05, respectively.

The test hypotheses are:

Null hypothesis:

*H*_{0}: *μ* = 2.7.

Alternative hypothesis:

*H*_{1}: *μ* ≠ 2.7.

Step 2

As the population standard deviation is unknown, the sample standard deviation must be used while performing the test. Thus, the suitable test to use here is the **one sample t test**.

Step-by-step procedure to find the test statistic using TI-84 calculator:

- Click on
**STAT > Tests> T-Test.** - Enter
**2.7**for**µ**,_{0}**2.74**for**x bar**,**0.05**for**S**and_{X}**80**for**n**. - Select
**µ ≠ µ**._{0} - Select
**Calculate**and**Enter.**

Output is obtained as follows:

Step 3

From the output, test statistic is approximately 7.155.

Here, the distribution is two tailed, the degrees of freedom is 79 (= 80 – 1) and the level of significance is 0.05.

The critical value using TI-84 is obtained as follows:

- Enter
**2nd > DISTR**. - Choose
**3: InvT(** - Enter
**area**as**1&...**

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