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)
What is the level of significance?
1. Hypothesis testing is a procedure based on sample evidence and probability theory to decide whether the hypothesis is a reasonable statement.
Answer: True. Hypothesis testing involves collecting sample evidence and using probability theory to determine if the hypothesis is plausible or not.
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: False. For a one-tailed test at a 0.05 level of significance, the critical value for the z test is 1.645, but for a t-test it depends on the degrees of freedom. In this case, if the sample size is large, the critical value for t would be close to 1.645, but generally, it would be higher than that.
3. An alternate hypothesis is a statement about a population parameter that is accepted when the null hypothesis is rejected.
Answer: False. An alternate hypothesis is a statement about a population parameter that is considered if there is enough evidence to reject the null hypothesis. 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: The computed t-value of 3.677 indicates that the sample average is significantly different from 22,100 miles. To determine if there is enough evidence to accept the manufacturer's claim, we would need to compare the calculated t-value with the critical t-value at the given significance level (0.05). If the calculated t-value is greater than the critical t-value, then there is enough evidence to reject the null hypothesis and accept the manufacturer's claim. Without the critical t-value, it is not possible to determine the correct answer.
5. The region or area of rejection defines the location of all those values that are so large or small that the probability of their occurrence under a true null hypothesis is rather remote.
Answer: True. The region of rejection in hypothesis testing defines the range of values that are considered extreme enough to provide evidence against the null hypothesis. It includes values that are either unusually high or unusually low.
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. In this scenario, the alternative hypothesis states that μ is less than 200, indicating a one-tailed test. A two-tail test would have an alternative hypothesis stating 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: False. Failing to reject the null hypothesis does not prove that the null hypothesis is true. It simply means that there is not enough evidence to reject it based on the available sample evidence.
8. The null hypothesis is rejected when a p-value is greater than a stated significance level.
Answer: False. The null hypothesis is rejected when the p-value is less than or equal to the stated significance level. This is because 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.
Explanation: The region of acceptance for a t-distribution will generally be smaller than for large samples. As the degrees of freedom increase, the t-distribution approaches the standard normal distribution, and the region of acceptance becomes narrower.
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 μ = 0.55, and the alternate is μ ≠ 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: Based on the given information, we can calculate the test statistic for testing the null hypothesis. Calculate the test statistic using the sample proportion:
test statistic = (sample proportion - hypothesized proportion) / sqrt((hypothesized proportion * (1 - hypothesized proportion)) / sample size)
test statistic = (228/400 - 0.55) / sqrt((0.55 * (1 - 0.55)) / 400)
Once you calculate the test statistic, you can compare it to the critical value(s) for a two-tailed test at the 0.01 significance level. If the test statistic falls within the rejection region, reject the null hypothesis; otherwise, do not reject it. The correct decision cannot be determined without knowing the critical value(s) for the given significance level.