In this problem, assume that the distribution of differences is approximately normal. Note: For degrees of freedom d.f. not in the Student's t table, use the closest d.f. that is smaller. In some situations, this choice of d.f. may increase the P-value by a small amount and therefore produce a slightly more "conservative" answer.i need help with c, sketching, d and e In this problem, assume that the distribution of differences is approximately normal. Note: For degrees of freedom d.f. not in the Student's t table, use the closest d.f. that is smaller. In some situations, this choice of d.f. may increase the P-value by a small amount and thereforeproduce a slightly more "conservative" answer.In the following data pairs, A represents the cost of living index for utilities and B represents the cost of living index for transportation. The data are paired by metropolitan areas in the United States. A random sample of 46 metropolitan areas gave the following information.A:B:90858410483100891251071008910510310910994115114A:В:118133104848077909290106951101121059311999109A:106951101121059311999109B:961091031071031021018694A:B:109113100901211208591919788104119116104121108869096Do the data indicate that the U.S. population mean cost of living index for utilities is less than that for transportation in these areas? Use a = 0.05. (Let d = A - B.)A:B:9511599868810680108871008310394125115100127(a) What is the level of significance?State the null and alternate hypotheses. Will you use a left-tailed, right-tailed, or two-tailed test?O Ho: Hd< 0; H: H= 0; left-tailedO Ho: Hd = 0; H;: Hd> 0; right-tailedO Ho: Hd = 0; H;: Hd < 0; left-tailedO Ho: Hd = 0; H: Hd# 0; two-tailed(b) What sampling distribution will you use? What assumptions are you making?O The standard normal. We assume that d has an approximately uniform distribution.O The standard normal. We assume that d has an approximately normal distribution.O The Student's t. We assume that d has an approximately normal distribution.O The Student's t. We assume that d has an approximately uniform distribution.What is the value of the sample test statistic? (Round your answer to three decimal places.)(c) Find (or estimate) the P-value.O P-value > 0.250O 0.125 < P-value < 0.250O 0.050 < P-value < 0.125O 0.025 < P-value < 0.050O 0.005 < P-value < 0.025O P-value < 0.005 Sketch the sampling distribution and show the area corresponding to the P-value.baO-4O-4-2CdO-4O-4(d) Based on your answers in parts (a) to (c), will you reject or fail to reject the null hypothesis? Are the data statistically significant at level a?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 fail to reject the null hypothesis and conclude the data are 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 not statistically significant.(e) State your conclusion in the context of the application.O Fail to reject the null hypothesis, there is sufficient evidence to claim that the mean cost of living index for utilities is less than that for transportation.O Reject the null hypothesis, there is sufficient evidence to claim that the mean cost of living index for utilities is less than that for transportation.O Reject the null hypothesis, there is insufficient evidence to claim that the mean cost of living index for utilities is less than that for transportation.O Fail to reject the null hypothesis, there is insufficient evidence to claim that the mean cost of living index for utilities is less than that for transportation.

Name: In this problem, assume that the distribution of differences is approx
Uploaded: 2024-03-20T07:07:12.000Z
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Description: In this problem, assume that the distribution of differences is approximately normal. Note: For degrees of freedom d.f. not in the Student's t table, use the closest d.f. that is smaller. In some situations, this choice of d.f. may increase the P-val