A consumer analyst reports that the mean life of a certain type of alkaline battery is no more than 63 months. Write the null and alternative hypotheses and note which is the claim.
A consumer analyst reports that the mean life of a certain type of alkaline battery is no more than 63 months. Write the null and alternative hypotheses and note which is the claim.
Ho: μ = 63 (claim), Ha: μ ≥ 63
Ho: μ ≤ 63 (claim), Ha: μ > 63
Ho: μ ≤ 63, Ha: μ > 63 (claim)
Ho: μ > 63 (claim), Ha: μ ≤ 63
Question 2An amusement park claims that the average daily attendance is at least 15,000. Write the null and alternative hypotheses and note which is the claim.
Ho: μ ≥ 15000 (claim), Ha: μ < 15000
Ho: μ = 15000, Ha: μ ≤ 15000 (claim)
Ho: μ > 15000 (claim), Ha: μ = 15000
Ho: μ ≤ 15000, Ha: μ > 15000 (claim)
Question 3If the null hypothesis is rejected when it is true, this is called __________.
>a type I error
the Empirical Rule
a type II error
an alternative hypothesis
Question 4A scientist claims that the mean gestation period for a fox is less than 50.3 weeks. If a hypothesis test is performed that rejects the null hypothesis, how would this decision be interpreted?
There is enough evidence to support the scientist’s claim that the gestation period is less than 50.3 weeks
There is not enough evidence to support the scientist’s claim that the gestation period is 50.3 weeks
The evidence indicates that the gestation period is more than 50.3 weeks
There is not enough evidence to support the scientist’s claim that the gestation period is more than 50.3 weeks
Question 5A marketing organization claims that 10% of its employees are paid minimum wage. If a hypothesis test is performed that fails to reject the null hypothesis, how would this decision be interpreted?
There is sufficient evidence to support the claim that 10% of the employees are paid minimum wage
There is not sufficient evidence to support the claim that less than 10% of the employees are paid minimum wage
There is not sufficient evidence to support the claim that 10% of the employees are paid minimum wage
There is sufficient evidence to support the claim that more than 10% of the employees are paid minimum wage
Question 6A sprinkler manufacturer claims that the average activating temperatures is at most 132 degrees. To test this claim, you randomly select a sample of 32 systems and find the mean activation temperature to be 133 degrees. Assume the population standard deviation is 3.3 degrees. Find the standardized test statistic and the corresponding p-value.
z-test statistic = 1.71, p-value = 0.0865
z-test statistic = -1.71, p-value = 0.0865
z-test statistic = 1.71, p-value = 0.0432
z-test statistic = -1.71, p-value = 0.0432
Question 7A consumer research organization states that the mean caffeine content per 12-ounce bottle of a population of caffeinated soft drinks is 37.8 milligrams. You find a random sample of 48 12-ounce bottles of caffeinated soft drinks that has a mean caffeine content of 32.8 milligrams. Assume the population standard deviation is 12.5 milligrams. At α=0.05, what type of test is this and can you reject the organization’s claim using the test statistic?
Claim is null, reject the null and reject claim as test statistic (-2.77) is in the rejection region defined by the critical value (-1.96)
Claim is alternative, reject the null and support claim as test statistic (-2.77) is in the rejection region defined by the critical value (-1.64)
Claim is alternative, fail to reject the null and support claim as test statistic (-2.77) is not in the rejection region defined by the critical value (-1.64)
Claim is null, fail to reject the null and reject claim as test statistic (-2.77) is not in the rejection region defined by the critical value (-1.96)
Question 8A computer manufacturer estimates that its cheapest screens will last less than 2.8 years. A random sample of 61 of these screens has a mean life of 2.4 years. The population is normally distributed with a population standard deviation of 0.88 years. At α=0.02, what type of test is this and can you reject the organization’s claim using the test statistic?
Claim is alternative, fail to reject the null and support claim as test statistic (-3.55) is in the rejection region defined by the critical value (-2.05)
Claim is alternative, reject the null and support claim as test statistic (-3.55) is in the rejection region defined by the critical value (-2.05)
Claim is null, fail to reject the null and cannot support claim as test statistic (-3.55) is in the rejection region defined by the critical value (-2.05)
Claim is null, reject the null and cannot support claim as test statistic (-3.55) is in the rejection region defined by the critical value (-2.05)
Question 9A business receives supplies of copper tubing where the supplier has said that the average length is 26.70 inches so that they will fit into the business’ machines. A random sample of 48 copper tubes finds they have an average length of 26.75 inches. The population standard deviation is assumed to be 0.15 inches. At α=0.05, should the business reject the supplier’s claim?
Yes, since p<α, we reject the null and the null is the claim
Yes, since p>α, we fail to reject the null and the null is the claim
No, since p>α, we reject the null and the null is the claim
No, since p>α, we fail to reject the null and the null is the claim
Question 10The company’s cleaning service states that they spend more than 46 minutes each time the cleaning service is there. The company times the length of 37 randomly selected cleaning visits and finds the average is 47.6 minutes. Assuming a population standard deviation of 5.2 minutes, can the company support the cleaning service’s claim at α=0.10?
No, since p>α, we fail to reject the null. The claim is the alternative, so the claim is not supported
Yes, since p<α, we reject the null. The claim is the alternative, so the claim is supported
Yes, since p>α, we fail to reject the null. The claim is the null, so the claim is supported
No, since p<α, we reject the null. The claim is the alternative, so the claim is not supported
Question 11A customer service phone line claims that the wait times before a call is answered by a service representative is less than 3.3 minutes. In a random sample of 62 calls, the average wait time before a representative answers is 3.26 minutes. The population standard deviation is assumed to be 0.14 minutes. Can the claim be supported at α=0.08?
No, since test statistic is in the rejection region defined by the critical value, reject the null. The claim is the alternative, so the claim is not supported
Yes, since test statistic is not in the rejection region defined by the critical value, reject the null. The claim is the alternative, so the claim is supported
No, since test statistic is not in the rejection region defined by the critical value, reject the null. The claim is the alternative, so the claim is not supported
Yes, since test statistic is in the rejection region defined by the critical value, reject the null. The claim is the alternative, so the claim is supported
Question 12In a hypothesis test, the claim is μ≤40 while the sample of 27 has a mean of 41 and a sample standard deviation of 5.9 from a normally distributed data set. In this hypothesis test, would a z test statistic be used or a t test statistic and why?
z test statistic would be used as the population standard deviation is known
z test statistic would be used as the mean is greater than 30
t test statistic would be used as the standard deviation is less than 10
t test statistic would be used as the data are normally distributed with an unknown population standard deviation
Question 13A university claims that the mean time professors are in their offices for students is at least 6.5 hours each week. A random sample of nine professors finds that the mean time in their offices is 6.2 hours each week. With a sample standard deviation of 0.49 hours from a normally distributed data set, can the university’s claim be supported at α=0.05?
Yes, since the test statistic is not in the rejection region defined by the critical value, the null is not rejected. The claim is the null, so is supported
Yes, since the test statistic is in the rejection region defined by the critical value, the null is not rejected. The claim is the null, so is supported
No, since the test statistic is in the rejection region defined by the critical value, the null is rejected. The claim is the null, so is not supported
No, since the test statistic is not in the rejection region defined by the critical value, the null is rejected. The claim is the null, so is not supported
Question 14A credit reporting agency claims that the mean credit card debt in a town is greater than $3500. A random sample of the credit card debt of 20 residents in that town has a mean credit card debt of $3600 and a standard deviation of $391. At α=0.10, can the credit agency’s claim be supported, assuming this is a normally distributed data set?
No, since p of 0.13 is greater than 0.10, fail to reject the null. Claim is alternative, so is not supported
No, since p-value of 0.13 is greater than 0.10, reject the null. Claim is null, so is not supported
Yes, since p-value of 0.13 is greater than 0.10, fail to reject the null. Claim is null, so is supported
Yes, since p-value of 0.13 is less than 0.55, reject the null. Claim is alternative, so is supported
Question 15A researcher wants to determine if daily walks together strengthen a marriage. One group of wives and one group of husbands are selected and take walks each day. After 2 weeks, all are asked if they felt their marriage was stronger based on the walks and the results of the two groups are compared. To be a valid matched pair test, what should the researcher consider in creating the two groups?
That all husbands and wives in the test had been married about the same amount of time
That the wives group was positive on marriage before the walks
That the husbands and wives selected were married to each other
That the both groups were positive on marriage before the walks
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