Question

For a random sample of 36 data pairs, the sample mean of the differences was 0.76. The sample standard deviation of the differences was 2. At the 5% level of significance, test the claim that the population mean of the differences is different from 0. (a) Is it appropriate to use a Student's t distribution for the sample test statistic? Explain. Yes, the sample size is larger than 30. Yes, the standard deviation is larger than the sample mean. No, the standard deviation is not smaller than the sample mean. No, the sample size is not larger than 30. What degrees of freedom are used? (b) State the hypotheses. H0: μd = 0; H1: μd ≠ 0 (c) Compute the t value. (Round your answer to three decimal places.) (d) Estimate the P-value of the sample test statistic. P-value > 0.500 0.250 < P-value < 0.500 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 the null hypothesis? Explain. 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 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 statistically significant. At the α = 0.05 level, we fail to reject the null hypothesis and conclude the data are not statistically significant. (f) What do your results tell you? Reject the null hypothesis, there is insufficient evidence to conclude that the population mean of the differences is not zero. Fail to reject the null hypothesis, there is sufficient evidence to conclude that the population mean of the differences is not zero.

          For a random sample of 36 data pairs, the sample mean of the differences was 0.76. The sample standard deviation of the differences was 2. At the 5% level of significance, test the claim that the population mean of the differences is different from 0.

(a) Is it appropriate to use a Student's t distribution for the sample test statistic? Explain.
Yes, the sample size is larger than 30. Yes, the standard deviation is larger than the sample mean. No, the standard deviation is not smaller than the sample mean. No, the sample size is not larger than 30.

What degrees of freedom are used?

(b) State the hypotheses.
H0: μd = 0; H1: μd ≠ 0

(c) Compute the t value. (Round your answer to three decimal places.)

(d) Estimate the P-value of the sample test statistic.
P-value > 0.500
0.250 < P-value < 0.500
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 the null hypothesis? Explain.
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 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 statistically significant.
At the α = 0.05 level, we fail to reject the null hypothesis and conclude the data are not statistically significant.

(f) What do your results tell you?
Reject the null hypothesis, there is insufficient evidence to conclude that the population mean of the differences is not zero.
Fail to reject the null hypothesis, there is sufficient evidence to conclude that the population mean of the differences is not zero.

Added by Jacob S.

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