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A random sample of 25 values is drawn from a mound-shaped and symmetric distribution.

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A random sample of 25 values is drawn from a mound-shaped and symmetric distribution. The sample mean is 11 and 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 is 10.5.

(a) Is it appropriate to use a Student’s t distribution? Explain. Yes, because the x distribution is mound-shaped and symmetric and σ is unknown. No, the x distribution is skewed left. No, the x distribution is skewed right. No, the x distribution is not symmetric. No, σ is known. How many degrees of freedom do we use?

 

(b) What are the hypotheses? H0: μ = 10.5; H1: μ < 10.5 H0: μ > 10.5; H1: μ = 10.5 H0: μ = 10.5; H1: μ > 10.5 H0: μ = 10.5; H1: μ ≠ 10.5 H0: μ < 10.5; H1: μ = 10.5

 

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

 

(d) Estimate the P-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 reject H0? At the α = 0.05 level, we reject the null hypothesis and conclude the data are statistically significant. At the α = 0.05 level, we reject the null hypothesis and conclude the data are not statistically significant. At the α = 0.05 level, we fail to reject the null hypothesis and conclude the data are statistically significant. At the α = 0.05 level, we fail to reject the null hypothesis and conclude the data are not statistically significant.

 

 
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