The 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 hypothesis

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Asked Oct 8, 2019
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The average salary for American college graduates is $43,900. You suspect that the average is different for graduates
from your college. The 65 randomly selected graduates from your college had an average salary of $43,580 and a
standard 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 use
t-test for a population mean
Но:
H1
c. The test statistic t 4 =
(please show your answer to 3 decimal places.)
d. The p-value
e. The p-value is
f. Based on this, we should fail to reject
g. Thus, the final conclusion is that ...
(Please show your answer to 4 decimal places.)
X
the null hypothesis
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The average salary for American college graduates is $43,900. You suspect that the average is different for graduates from your college. The 65 randomly selected graduates from your college had an average salary of $43,580 and a standard 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 use t-test for a population mean Но: H1 c. The test statistic t 4 = (please show your answer to 3 decimal places.) d. The p-value e. The p-value is f. Based on this, we should fail to reject g. Thus, the final conclusion is that ... (Please show your answer to 4 decimal places.) X the null hypothesis

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Expert Answer

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:

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Sample statistic Null Parameter t = SE 43,900 43,580 6,730 65 =0.383

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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:

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StatKey Theoretical Distribution TDistributi 40 631 31 40 40 1.0 20 833

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Step 3

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

(e)

...
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If p-value significance level, reject the null hypothesis If p-value> significance level, do not reject the null hypothesis.

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Hypothesis Testing

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