PLEASE CHECK AND SEE IF I HAVE THESE ANSWERS CORRECT.

T F 1. Hypothesis testing is a procedure based on sample evidence and probability theory to decide whether the hypothesis is a reasonable statement.

ANSWER (True)


T F 2. For a one-tailed test using the 0.05 level of significance, the critical value for the z test is 1.645, but for t it is 1.96.
ANSWER (True)


T F 3. An alternate hypothesis is a statement about a population parameter that is accepted when the null hypothesis is rejected.
ANSWER (False)

T F 4. Records on a fleet of trucks reveal that the average life of a set of spark plugs is normally distributed with a mean of 22,100 miles. A manufacturer of spark plugs claims that its plugs have an average life in excess of 22,100 miles. The fleet owner purchased 18 sets and found that the sample average life was 23,400 miles, the sample standard deviation was 1,500 miles and the computed t = 3.677. Based on these findings, there is enough evidence to accept the manufacturer's claim at the 0.05 level.
ANSWER (True)


T F 5. The region or area of rejection defines the location of all those values that are so large or so small that the probability of their occurrence under a true null hypothesis is rather remote.
ANSWER (True)

T F 6. If the null hypothesis is ƒÝ„d 200 and the alternate hypothesis states that ƒÝ is less than 200, then, a two-tail test is being conducted. (ANSWER (False)

T F 7. If we do not reject the null hypothesis based on sample evidence, we have proven beyond doubt that the null hypothesis is true. ANSWER(True)

T F 8. The null hypothesis is rejected when a p-value is greater than a stated significance level.
ANSWER (True)

9. Which of the following does NOT hold true for the t distribution?
A) Confidence intervals will be wider than for large samples.
B) The region of acceptance will be larger than for large samples.
C) A larger computed t value will be needed to reject the null hypothesis than for large samples using z.
D) There is only one t distribution.

ANSWER (B)
10. Test at the 0.01 level the statement that 55% of those families who plan to purchase a vacation residence in Florida want a condominium. The null hypothesis is ƒà = 0.55 and the alternate is ƒà„j 0.55. A random sample of 400 families who planned to buy a vacation residence revealed that 228 families want a condominium. What decision should be made regarding the null hypothesis?
A) Do not reject it
B) Reject it
C) Cannot accept nor reject it based on the information given
D) None of the above
ANSWER (a)

1. Correct. Hypothesis testing is a procedure based on sample evidence and probability theory to decide whether the hypothesis is a reasonable statement.

2. Correct. For a one-tailed test using the 0.05 level of significance, the critical value for the z test is 1.645 and for the t test it is 1.96.
3. Incorrect. An alternate hypothesis is a statement about a population parameter that is accepted when the null hypothesis is rejected.
4. Correct. Based on the given information, there is enough evidence to accept the manufacturer's claim at the 0.05 level.
5. Correct. The region or area of rejection defines the location of all those values that are so large or so small that the probability of their occurrence under a true null hypothesis is rather remote.
6. Incorrect. If the null hypothesis is ƒÝ = 200 and the alternate hypothesis states that ƒÝ is less than 200, then a one-tail test is being conducted.
7. Incorrect. If we do not reject the null hypothesis based on sample evidence, it does not prove beyond doubt that the null hypothesis is true. It simply means that we do not have enough evidence to reject it.
8. Correct. The null hypothesis is rejected when a p-value is smaller than the stated significance level.
9. Correct. The statement that does not hold true for the t distribution is B) The region of acceptance will be larger than for large samples.
10. Correct. Based on the given information, the decision should be to not reject the null hypothesis.

To check if your answers are correct, let's go through each question one by one:

1. Hypothesis testing is a procedure based on sample evidence and probability theory to decide whether the hypothesis is a reasonable statement.
- ANSWER (True)
- This statement is correct. Hypothesis testing is indeed a procedure that uses sample evidence and probability theory to make conclusions about a population.

2. For a one-tailed test using the 0.05 level of significance, the critical value for the z-test is 1.645, but for t it is 1.96.
- ANSWER (True)
- This statement is correct. The critical value for a one-tailed test at a significance level of 0.05 is 1.645 for the z-test and 1.96 for the t-test.

3. An alternate hypothesis is a statement about a population parameter that is accepted when the null hypothesis is rejected.
- ANSWER (False)
- This statement is incorrect. An alternate hypothesis is a statement about a population parameter that is considered when the null hypothesis is rejected. It is not automatically accepted when the null hypothesis is rejected.

4. Records on a fleet of trucks reveal that the average life of a set of spark plugs is normally distributed with a mean of 22,100 miles. A manufacturer of spark plugs claims that its plugs have an average life in excess of 22,100 miles. The fleet owner purchased 18 sets and found that the sample average life was 23,400 miles, the sample standard deviation was 1,500 miles, and the computed t-value was 3.677. Based on these findings, there is enough evidence to accept the manufacturer's claim at the 0.05 level.
- ANSWER (True)
- This statement is correct. To determine whether there is enough evidence to accept the manufacturer's claim, we need to perform a hypothesis test. Given the sample average life, sample standard deviation, and computed t-value, if the p-value is less than the significance level (0.05), then we can reject the null hypothesis and conclude that there is enough evidence to accept the manufacturer's claim.

5. The region or area of rejection defines the location of all those values that are so large or so small that the probability of their occurrence under a true null hypothesis is rather remote.
- ANSWER (True)
- This statement is correct. The region or area of rejection in hypothesis testing defines the range of values that are considered unlikely to occur if the null hypothesis is true. This region determines the critical values used to make decisions about rejecting or not rejecting the null hypothesis.

6. If the null hypothesis is μ ≥ 200 and the alternate hypothesis states that μ is less than 200, then a two-tail test is being conducted.
- ANSWER (False)
- This statement is incorrect. If the alternate hypothesis states that μ is less than 200 and the null hypothesis is μ ≥ 200, then a one-tail test is being conducted, not a two-tail test. A two-tail test would have the alternate hypothesis stating that μ is not equal to 200.

7. If we do not reject the null hypothesis based on sample evidence, we have proven beyond doubt that the null hypothesis is true.
- ANSWER (True)
- This statement is correct. Failing to reject the null hypothesis based on sample evidence does not definitively prove that the null hypothesis is true. It only means that there is insufficient evidence to reject it.

8. The null hypothesis is rejected when a p-value is greater than a stated significance level.
- ANSWER (True)
- This statement is correct. In hypothesis testing, the null hypothesis is rejected when the p-value (probability value) is less than or equal to the stated significance level. A smaller p-value indicates stronger evidence against the null hypothesis.

9. Which of the following does NOT hold true for the t-distribution?
- ANSWER (B) The region of acceptance will be larger than for large samples.
- This statement is correct. In hypothesis testing, as the sample size increases, the region of acceptance becomes narrower, not larger. Therefore, option B does not hold true for the t-distribution.

10. Test at the 0.01 level the statement that 55% of those families who plan to purchase a vacation residence in Florida want a condominium. The null hypothesis is p = 0.55 and the alternate is p ≠ 0.55. A random sample of 400 families who planned to buy a vacation residence revealed that 228 families want a condominium. What decision should be made regarding the null hypothesis?
- ANSWER (A) Do not reject it
- To test the statement, we need to calculate the test statistic and compare it to the critical value(s) corresponding to the chosen significance level (0.01). However, the information given does not provide the necessary values to calculate the test statistic or determine the decision regarding the null hypothesis. Therefore, based on the information given, we cannot accept or reject the null hypothesis (option C: Cannot accept nor reject it based on the information given).

Overall, you have 7 out of 10 correct answers.