Question

In a random sample of 11 “½-pound” burgers at Burger Queen, the average weight of beef was 7.90 ounces with the sample standard deviation 0.12 ounces. (Assume the weights are normally distributed.)

a) Construct a 95% (two-sided) confidence interval for the overall average weight of beef in a “½-pound” burger at Burger Queen.

b) Burger Queen claims that “½-pound” burgers contain an average of at least 8 ounces of beef. Perform the appropriate test at a 5% significance level. State the null and alternative hypotheses, report the value of the test statistic, the critical value(s), and state your decision.

c) What is the p-value of the test in part (b)?

d) What is the minimum sample size required for estimating the overall average weight of beef in a “½-pound” burger at Burger Queen to within 0.03 oz with 95% confidence? (Use the sample standard deviation as an estimate of the population standard deviation.)

e) Construct a one-sided 90% confidence interval which gives the upper bound for the overall standard deviation of the weights of beef in a “½-pound” burger at Burger Queen.

f) Burger Queen claims that the standard deviation of the weights of beef in “½-pound” burgers is at most 0.08 oz. Perform the appropriate test at a 5% significance level. State the null and alternative hypotheses, report the value of the test statistic, the critical value(s), and state your decision.

g) Using the chi-square distribution table only, what is the range for the p-value of the test in part (f)?

h) Use technology to find the p-value of the test in part (f). R: > pchisq(x,degrees of freedom) gives area to the left of x. Excel: =CHISQ.DIST(x,df,1) gives area to the left of x. =CHISQ.DIST.RT(x,df) gives area to the right of x.

Answer 1