1.Use the t-distribution to find a confidence interval for a mean μ

given the relevant sample results. Give the best point estimate for μ, the margin of error, and the confidence interval. Assume the results come from a random sample from a population that is approximately normally distributed.

A 90% confidence interval for μ using the sample results x¯=137.0, s=56.2, and n=50

Round your answer for the point estimate to one decimal place, and your answers for the margin of error and the confidence interval to two decimal places.

point estimate = 137

1a) margin of error = __________

1b) The 90% confidence interval is _________ to ________

2.Use a t-distribution to find a confidence interval for the difference in means μd=μ1-μ2 using the relevant sample results from paired data. Assume the results come from random samples from populations that are approximately normally distributed, and that differences are computed using d=x1-x2

A 99% confidence interval for μd using the paired data in the following table:
Case 1 2 3 4 5

Treatment 22 28 31 25 27
1

Treatment 17 31 24 20 20
2

Give the best estimate for μd, the margin of error, and the confidence interval.

Enter the exact answer for the best estimate, and round your answers for the margin of error and the confidence interval to two decimal places.

2a) best estimate = _________

2b) margin of error = _________

2c) The 99% confidence interval is ______ to _______

3.Use a t-distribution and the given matched pair sample results to complete the test of the given hypotheses. Assume the results come from random samples, and if the sample sizes are small, assume the underlying distribution of the differences is relatively normal. Assume that differences are computed using d=x1-x2
Test H0 : μd=0 vs Ha : μd≠0 using the paired difference sample results x¯d=13.84, sd=12.7, nd=25

Give the test statistic and the p-value.
Round your answer for the test statistic to two decimal places and your answer for the p-value to three decimal places.

test statistic = 5.45

11a) p-value = ________

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