# Hypothesis and Error Type Questions

1. Using rare event rule and subjective estimates to determine whether events are likely. Claim: People born on February 29 have IQ scores that vary less than the general population for which the sigma = 15, and a random sample of 50 people born on February 29 results in IQ scores with s= 14.99.

2. Identify H0 and H1 in symbolic form for the following statement.

The proportion of people in California who enjoy western movies is less than 50%.

H0:

H1:

3. Identify H0 and H1 in symbolic form for the following statement.

The mean length of telephone calls at the girls' dormitory of Stonehurst College is more than 10 minutes.

H0:

H1:

4. Identify H0 and H1 in symbolic form for the following statement.

Salaries among bank tellers at National Bank have a standard deviation of $500.

H0:

H1:

5. Assume a normal distribution. Find the critical value for a left-tailed test where = 0.005.

6. Assume a normal distribution. Find the critical value for a right-tailed test where = 0.025.

7. Assume a normal distribution. Find the critical value for a two-tailed test where = 0.02.

8. Identify the type I error and the type II error corresponding to the following claim.

"The mean age of certified public accountants is greater than 32 years."

Type I:

Type II:

9. Identify the type I error and the type II error corresponding to the following claim.

"The proportion of American men who like football is 70%."

Type I:

Type II:

10.Find the P-value for a right-tailed test in which z = 0.26. Show or explain procedure.

11. Find the P-value for a left-tailed test in which z = -1.34. Show or explain procedure.

12. Find the P-value for a two-tailed test in which z = -2.48. Show or explain procedure.

13. Find the P-value for a test with H1: p 0.45, and the test statistic is z = 1.25. Show or explain your procedure.

14. State the final conclusion regarding the claim in non-technical terms.

Original Claim: "The proportion of smokers who like filtered king-sized cigarettes is equal to 85%."

Initial Conclusion: "Fail to reject the null hypothesis."

15. State the final conclusion regarding the claim in non-technical terms.

Original Claim: "The mean length of time for students at Givens College to complete their bachelor's degree is less than four years."

Initial Conclusion: "Reject the null hypothesis."

16. Find the value of the test statistic. The claim is that the proportion of women employed in the clothing industry is 0.6. A random sample of 80 clothing industry employees reveals that 67.5% are women.

(Substitute values into the equation and solve for z).

#### Solution Preview

Please see the attached file.

1. Using rare event rule and subjective estimates to determine whether events are likely. Claim: People born on February 29 have IQ scores that vary less than the general population for which the sigma = 15, and a random sample of 50 people born on February 29 results in IQ scores with s= 14.99.

Null hypothesis H0:

Alternative hypothesis H1:

Use chi-squared test, we can compute the test statistic

So, the p-value is

Since p-value is very big, we fail to reject the null hypothesis H0: . We conclude that "People born on February 29 have IQ scores that vary less than the general population for which the sigma = 15" is incorrect.

2. Identify H0 and H1 in symbolic form for the following statement.

The proportion of people in California who enjoy western movies is less than 50%.

H0: p=50%

H1: p<50%

3. Identify H0 and H1 in symbolic form for the following statement.

The mean length of telephone calls at the girls' dormitory of Stonehurst College is more than 10 minutes.

H0:

H1:

4. Identify H0 and H1 in symbolic form for the following statement.

Salaries among bank tellers at National Bank have a standard deviation of $500.

H0:

H1:

5. Assume a normal distribution. Find the critical value for a left-tailed test

where = 0.005.

6. Assume a normal distribution. Find the critical value for a ...

#### Solution Summary

Solution answers 16 questions on refining and evaluating hypothesis (including H1 and H0s) and error typing in a Word attachment.