For a random sample of 36 data pairs, the sample mean of the differences was 0.77. 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.

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For a random sample of 36 data pairs, the sample mean of the differences was 0.77. 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.

I need help with d e and f

(a) Is it appropriate to use a Student's t distribution for the sample test statistic? Explain.
O Yes, the sample size is larger than 30.
O No, the standard deviation is not smaller than the sample mean.
O Yes, the standard deviation is larger than the sample mean.
O No, the sample size is not larger than 30.
What degrees of freedom are used?
(b) State the hypotheses.
O Ho: Ha = 0; H,: H# 0
O Ho: Hd = 0; H1: Hd>0
O Ho: Hd = 0; H4: Hd <0
O Ho: Hg# 0; Hq: Hd = 0
(c) Compute the t value. (Round your answer to three decimal places.)
(d) Estimate the P-value of the sample test statistic.
O P-value > 0.500
O 0.250 < P-value < 0.500
O 0.100 < P-value < 0.250
O 0.050 < P-value < 0.100
O 0.010 < P-value < 0.050
O p-value < 0.010
(e) Do we reject or fail to reject the null hypothesis? Explain.
O At the a = 0.05 level, we reject the null hypothesis and conclude the data are not statistically significant.
O At the a = 0.05 level, we reject the null hypothesis and conclude the data are statistically significant.
O At the a = 0.05 level, we fail to reject the null hypothesis and conclude the data are statistically significant.
O At the a = 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?
O Fail to reject the null hypothesis, there is sufficient evidence to conclude that the population mean of the differences is not zero.
O Reject the null hypothesis, there is sufficient evidence to conclude that the population mean of the differences is not zero.
O Fail to reject the null hypothesis, there is insufficient evidence to conclude that the population mean of the differences is not zero.
O Reject the null hypothesis, there is insufficient evidence to conclude that the population mean of the differences is not zero.
Transcribed Image Text:(a) Is it appropriate to use a Student's t distribution for the sample test statistic? Explain. O Yes, the sample size is larger than 30. O No, the standard deviation is not smaller than the sample mean. O Yes, the standard deviation is larger than the sample mean. O No, the sample size is not larger than 30. What degrees of freedom are used? (b) State the hypotheses. O Ho: Ha = 0; H,: H# 0 O Ho: Hd = 0; H1: Hd>0 O Ho: Hd = 0; H4: Hd <0 O Ho: Hg# 0; Hq: Hd = 0 (c) Compute the t value. (Round your answer to three decimal places.) (d) Estimate the P-value of the sample test statistic. O P-value > 0.500 O 0.250 < P-value < 0.500 O 0.100 < P-value < 0.250 O 0.050 < P-value < 0.100 O 0.010 < P-value < 0.050 O p-value < 0.010 (e) Do we reject or fail to reject the null hypothesis? Explain. O At the a = 0.05 level, we reject the null hypothesis and conclude the data are not statistically significant. O At the a = 0.05 level, we reject the null hypothesis and conclude the data are statistically significant. O At the a = 0.05 level, we fail to reject the null hypothesis and conclude the data are statistically significant. O At the a = 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? O Fail to reject the null hypothesis, there is sufficient evidence to conclude that the population mean of the differences is not zero. O Reject the null hypothesis, there is sufficient evidence to conclude that the population mean of the differences is not zero. O Fail to reject the null hypothesis, there is insufficient evidence to conclude that the population mean of the differences is not zero. O Reject the null hypothesis, there is insufficient evidence to conclude that the population mean of the differences is not zero.
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