1. A machine produces 3-inch nails. A sample of 10 nails was selected and the lengths determined. The results are as follows: XXXXXXXXXX XXXXXXXXXX &n bsp; XXXXXXXXXX Use these results to test H0: mu...

1. A machine produces 3-inch nails. A sample of 10 nails was selected and the lengths determined. The results are as follows:

2.89 2.95 3.00 3.05 2.99 2.96 3.10 3.06 &n bsp; 3.00 3.12

Use these results to test H0: mu = 3 and Ha: mu ?(does not equal) 3 at ?simga = 0.01. Give the critical region, the computed test statistic, and the conclusion.



2. A machine produces 3-inch nails. A sample of 100 nails is selected, and it is found that 25 are shorter than 3 inches. Find the 95% confidence interval on the proportion of all such nails that are shorter than 3 inches



3. A sample of size n = 14 is selected from a normal population to construct a 95% confidence interval estimate for a population mean. The interval was computed to be (7.82 to 9.64). Determine the sample standard deviation.



4. Determine the p-value for each of the following hypothesis-testing situations:

a. H0: p = 0.25 and Ha: p ?(does not equal) 0.25; z test value = 1.84

b. H0: mu ? 13.5 and Ha: mu


5. An insurance company states that 90% of its claims are settled within 5 weeks. A consumer group selected a random sample of 100 of the company’s claims and found 75 of the claims were settled within 5 weeks. Is there enough evidence to support the consumer group’s claim that fewer than 90% of the claims were settled within 5 weeks? Test using the traditional approach with ?sigma = 0.05



6. A random sample of 51 observations was selected from a normally distributed population. The sample mean was xbar= 88.6, and the sample variance was s2 = 38.2. Does the sample show sufficient reason to conclude that the population standard deviation is not equal to 8 at the 0.05 level of significance? Use the p-value method.





8. The number of sit-ups that a person can do in one minute, both before and after a physical fitness course was recorded. The data is shown below for 10 randomly selected participants. Is there sufficient evidence to conclude that a significant amount of improvement took place? Assume variable is normally distributed. Test using ? = 0.01.



Before 30 23 25 29 27 25 30 &n bsp; 45 34 26

After 31 27 25 35 34 35 32 &nb sp; 52 50 43





9. You are given the following data. Test the claim that there is a difference in the means of the two groups. Use ? sigma= 0.10.



Group A Group B

Xbar = 2 xbar2 = 1.7

S2 = 0.6 S2 = 0.7

n1 = 120 n2 = 34