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1. A sample of 40 ten-year-old girls was taken and the weights of the girls recorded. The weights were used to find the sample mean weight of 71.5 pounds and the sample standard deviation of 12 pounds.

a. Find the 90% confidence interval estimate for the true mean weight of ten-year-old girls.

b. Find the 95% confidence interval estimate for the true mean weight of ten-year-old girls.

c. Find the 99% confidence interval estimate for the true mean weight of ten-year-old girls.

d. How do the widths of the confidence interval change as the level of confidence increases from 90 to 95 to 99?Which one of the following is correct?________________

(i)There is no difference between the widths

(ii)The confidence intervals become narrower when the level of confidence is increased

(iii)The confidence interval becomes wider as the level of confidence is increased.

2. A study was conducted to estimate the hospital costs for accident victims who wore seat belts. Twenty randomly selected cases have a mean of $9000 and standard deviation of $3000.

1. Construct a 95% CI for the mean of all such costs. (copy Minitab results below)

b.Write the CI from 2a in the form:Point Estimate +/- Margin of Error

c.Interpret the 95% confidence interval. Choose the best answer below.

i.The probability that the confidence interval contains the population mean is 0.95.

ii.If many samples of the same size were drawn from this population, and a confidence interval is calculated from each one, about 95% of those intervals would contain the population mean.

iii.A level 0.95 confidence interval is an interval with a margin of error 0.95, which is also correct 95% of the time.

3. The website (https://news.gallup.com/poll/166553/less-recommended-amount-sleep.aspx states that the average number of hours of sleep for Americans is 6.8 hrs.A researcher wants to test the claim that the average number of hours of the sleep for the second shift workers is less than the national average.A survey of 50 second shift workers revealed the average (mean) number of hours of sleep is 6 hrs, with the standard deviation of 0.5 hrs. Test the researcher's claim.

a. Are we testing for <, >, or ?

b. What is the population mean, ?

c. What is the value of the sample mean?

d Write the null and the alternate hypothesis:

H₀:

H_a:

e. Use Minitab for the Hypothesis Testing ( 1-sample t) (Copy your results below)

f. What is the t-value?

g .What is the p-value?

h. Is the p-value<0.05?

i.Does the p-value support claim?(Note: We conclude that the mean is significantly smaller if the p-value is <0.05).

j.Conclusion

4.Doctors recorded the head circumference (at birth) of 15 newborn boys. The mean was 33.798 centimeters, the standard deviation 0.630 centimeters. Use this to test the following hypotheses that the mean head circumference is equal to 34.5 cm.(Use the level of significance, = 0.05).Using Minitab, test the hypothesis (1-sample t-test)

a. Are we testing for <, >, or ?

b. What is the population mean, ?

c. What is the value of the sample mean?

d Write the null and the alternate hypothesis:

H₀:

H_a:

e. Use Minitab for the Hypothesis Testing ( 1-sample t) (Copy your results below)

f. What is the t-value?

g .What is the p-value?

h. Is the p-value<0.05?

i.Does the p-value support claim?(Note: We conclude that the mean is significantly smaller if the p-value is <0.05).

j. Conclusion