# Hypothesis Claim Testing

1. At a large publishing company, the mean age of proofreaders is 36.2 years with a standard deviation of 3.7 years. Assuming the age is normally distributed, find the following:

a. If a proofreader is selected at random what is probability his/her age will be between 36 and 38 years.

b. If a random selected sample 20 proofreaders is selected, what is the probability the mean of the sample will be 37 years?

2. The growing season for a random sample of 28 cities were recorded, yielding a sample mean of 190.7 days and a standard deviation of 54.2 days. Estimate the true proportion mean length of the growing season with 90% confidence.

3. A survey of 50 people after their first hang gliding experience showed that 21 would not want to hang glide again

c. Find the 90% confidence interval for the true proportion of people who would not hang glide a second time.

d. If 325 people go hang gliding for the first time, estimate the largest number of people who would repeat the experience?

4. In a random sample of 70 bolts, the mean length was 1.25 inches and the standard deviation was 0.01 inch. Find the 95% confidence interval of the true mean length of the bolt.

5. A scientist estimates that the mean nitrogen dioxide level in West London is greater than 28 parts per billion. Conduct a hypothesis test of this claim at the alpha =0.10 level using the data of 30 random days nitrogen dioxide level. Show the critical region and critical value

27 29 53 31 16 47 22 17 13 46

15 20 17 28 10 14 9 35 29 32

24 31 43 29 12 39 65 94 12 99

Hb : (English) Ha: (Math)

H0 : (English) H0: (Math)

Critical Area/s and Critical Values/s

Test Statistics

Decision

Conclusion

#### Solution Summary

This solution contains step-by-step calculations to determine the probability, mean of sample, true proportion mean length, true mean, and a hypothesis test.