1.Cost of Braces The average cost for teeth straightening with metal braces is approximately $5421. A nationwide franchise thinks that its cost is below that figure. A random sample of 28 patients across the country had an average cost of $5346 with a standard deviation of $630. At =0.10, can it be concluded that the mean is less than $5421? Assume that the population is approximately normally distributed.

(a) State the hypotheses and identify the claim.

H0: = $5421 not claim

H1 : < $5421 claim

This hypothesis test is a one-tailed test.

(b) Find the critical value(s). Round the answer(s) to at least three decimal places. If there is more than one critical value, separate them with commas. Critical value(s):?

2.Number of Words in a Novel The National Novel Writing Association states that the average novel is at least 50,000 word. A particularly ambitious writing club at a college-preparatory high school had randomly selected members with works of the following lengths. At =0.05, is there sufficient evidence to conclude that the mean length is greater than 50,000 word? Assume that the population is approximately normally distributed.

50,353 52,156 51,287 52,453 51,407 52,232 51,912

(a) State the hypotheses and identify the claim.

H0: =50000 not claim

H1: >50000 claim

This hypothesis test is a one-tailed test.

(b) Find the critical value(s). Round the answer(s) to at least three decimal places. If there is more than one critical value, separate them with commas. Critical value(s):?