A random sample of36values is drawn from a mound-shaped and symmetric distribution. The sample mean is13and the sample standard deviation is 2. Use a level of significance of 0.05 to conduct a two-tailed test of the claim that the population mean is12.5.

(a) Is it appropriate to use a Student'stdistribution? Explain.

Yes, because thexdistribution is mound-shaped and symmetric andis unknown.

No, thexdistribution is skewed left.

No, thexdistribution is skewed right.

No, thexdistribution is not symmetric.

No,is known.

How many degrees of freedom do we use?

(b) What are the hypotheses?

H₀:= 12.5;H₁:12.5

H₀:> 12.5;H₁:= 12.5

H₀:< 12.5;H₁:= 12.5

H₀:= 12.5;H₁:< 12.5

H₀:= 12.5;H₁:> 12.5

(c) Compute thetvalue of the sample test statistic. (Round your answer to three decimal places.)

t=

(d) Estimate theP-value for the test.

P-value > 0.250

0.100 <P-value < 0.250

0.050 <P-value < 0.100

0.010 <P-value < 0.050

P-value < 0.010

(e) Do we reject or fail to rejectH₀?

At the= 0.05 level, we reject the null hypothesis and conclude the data are statistically significant.

At the= 0.05 level, we reject the null hypothesis and conclude the data are not statistically significant.

At the= 0.05 level, we fail to reject the null hypothesis and conclude the data are statistically significant.

At the= 0.05 level, we fail to reject the null hypothesis and conclude the data are not statistically significant.

(f) Interpret the results.

There is sufficient evidence at the 0.05 level to reject the null hypothesis.

There is insufficient evidence at the 0.05 level to reject the null hypothesis.