Posted: August 4th, 2022

Statistics assignment

This is  introductory statistics questions. (STAT 230)

I’m looking for a statistic expert who always deliverys on time and has higher review scores.

I attached my homework which requires answers with solutions(how to get answers).

I live in Chicago so that it’s due by 22:00 today. (about 11 hrs left.)

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1.A survey of American planning long summer vacations in 2002 revealed a mean planned expenditure of \$1076. Assume that this mean is based on a random sample of 300 Americans who were planning long summer vacations in 2002 and that the sample standard deviation was \$345.

a) What is the point estimate of the mean planned expenditure by all Americans taking long summer vacations in 2002?

b) What is the 95% margin of error for the above mean planned expenditure?

c) Construct a 99% confidence interval for the mean planned expenditure of 2002

d) What does the 99% confidence interval mean in this context?

e) What is the maximum error (margin of error) estimate for part c)?

Suppose the standard deviation of all American’s planned expenditure of 2002 is believed to be \$400

according to some experts.

f) What, then, is the 99% confidence interval for the mean planned expenditure of 2002?

g) What is the maximum error (margin of error) of estimate for part f)

2. It is claimed that a new treatment is more effective than the standard treatment for prolonging the lives

of terminal cancer patients. The standard treatment has been in use for a longtime, and from records in

medical journals, the mean survival period is known to be 4.2 years. The new treatment is administered to

80 patients and their duration of survival recorded. The sample mean and the standard deviation are found

to be 4.5 and 1.1 years, respectively. Answer the following questions.

a) Define the 𝜇 in the context of this problem.

b) Formulate the null and alternative hypotheses

c) Is the alternative one-sided or two-sided?

d) State the Type I error and Type II error for this problem and tell why Type I error is more serious.

e) State the Z-test statistic for this problem and tell is distribution

f) Is the small, large or both small and large value of the Z-test that will lead us to reject the null hypothesis?

g) Suppose the significance level is 0.05. Determine the critical value for the rejection region and write

down the decision rule.

h) Calculate the value of Z-test statistics from the available data.

i) Determine whether or not the null hypothesis is rejected at the significance level and tell why.

j) Calculate the P-value and do the hypothesis testing based on the P-value

k) Express the conclusion in the context of the problem, using common English

3. A steel factory produces iron rods that are supposed to be 36 inches long. The machine that makes these

rods does not produce each rod exactly 36 inches long. The lengths of these rods vary slightly. It is known

that when the machine is working properly, the mean length of the rods is 36 inches. According to the design, the standard deviation of the lengths of all rods produced on this machine is always equal to 0.05 inches. The quality control department at the factory takes a sample of 40 such rods each week, calculates the mean length of these rods, and tests the null hypothesis 𝜇 = 36 inches against the alternative hypothesis 𝜇 ≠ 36 inches using 1% significance level. If the null hypothesis is rejected, the machine is stopped and adjusted.

A recent sample of 40 such rods produced a mean length of 36.015 inches.

a) Write down the null and alternative hypotheses.

b) Is the alternative one-sided or two-sided?

c) State the Type I error and Type II error for this problem and tell why Type I error is more serious.

d) State the Z-test statistic for this problem and tell is distribution

e) Is the small, large or both small and large value of the Z-test that will lead us to reject the null hypothesis?

f) Suppose the significance level is 0.05. Determine the critical value for the rejection region and write

down the decision rule.

g) Calculate the value of Z-test statistics from the available data.

h) Determine whether or not the null hypothesis is rejected at the significance level and tell why.

i) Calculate the P-value and do the hypothesis testing based on the P-value

j) Express the conclusion in the context of the problem, using common English.

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