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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.

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