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StatisticsQ&A LibraryThe average salary for American college graduates is $43,900. You suspect that the average is different for graduatesfrom your college. The 65 randomly selected graduates from your college had an average salary of $43,580 and astandard deviation of $6,730. What can be concluded at thee a =0.05 level of significance?a. For this study,b. The null and alternative hypotheses would be:we should uset-test for a population meanНо:H1c. The test statistic t 4 =(please show your answer to 3 decimal places.)d. The p-valuee. The p-value isf. Based on this, we should fail to rejectg. Thus, the final conclusion is that ...(Please show your answer to 4 decimal places.)Xthe null hypothesisQuestion

Asked Oct 8, 2019

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Step 1

(a)

The conditions for the t-distribution is appropriate as given below:

- If the sample size is larger (n≥30) or the distribution follows normal, then the t-distribution is appropriate.
- If the sample size is small and heavy skewness with outliers, then the t-distribution is not appropriate.

Here, the sample size is larger (n(=65)≥30). Hence, the condition for normality is satisfied. Thus, the t-distribution is appropriate.

(b)

The hypotheses are given below:

Null hypothesis:

H0:μ=$43,900

Alternative hypothesis:

H1:μ≠$43,900

(c)

The test statistic is obtained as follows:

Step 2

Thus, the test statistic is **0.383**.

(d)

The degrees of freedom is obtained as follows:

*p-value:*

Step-by-step procedure to obtain the p-value using StatKey:

- Choose
**t**under**Theoretical Distributions**. - In
**degrees of freedom**enter**64**and click**Ok**. - Click
**Two Tail**. - In
**Custom cutoff,**enter the numerical cutoff value as**–4.45**. - Click
**OK**.

Output obtained using StatKey is as follows:

Step 3

From the output, the p-value is **0.702 (=0.351*2)**.

(e)

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