Arithmetic Mean and Five-step P-value Approach
Sample
9.23
A manufacturer of chocolate candies uses machines to package candies as they move along a filling line. Although the packages are labeled as 8 ounces, the company wants the packages to contain a mean of 8.17 ounces so that virtually none of the packages contain less than 8 ounces. A sample of 50 packages is selected periodically, and the packaging process is stopped if there is evidence that the mean amount packaged is different from 8.17 ounces. Suppose that in a particular of 50 packages, the mean amount dispensed is 8.159 ounces, with a sample standard deviation of 0.051
A. Is there evidence that the population mean amount is different from 8.17 ounces? (Use a 0.05 level of significance.)
B. Determine the p-value and interpret its meaning.
9.27
In New York State, savings banks are permitted to sell a form of life insurance called savings bank life insurance (SLBI). The approval process consists of underwriting, which includes a review of the application, a medical information bureau check, possible requests for additional medical information and medical exams, and a policy complication stage in which the policy pages are generated and sent to the bank for delivery. The ability to deliver approved policies to customers in a timely manner is critical to the profitability of this service. During a period of one month, a random sample of 27 approved policies is selected, and the total processing time, in days, is recorded (and stored in insurance):
73
19
16
64
28
28
31
90
60
56
31
56 22 18
45
48
17
17
17
91
92
63
50
51
69
16 17
A. In the past, the mean processing time was 45 days. At the 0.05 level of significance, is there evidence that the mean processing time had changed from 45 days?
B. What assumption about the population distribution is needed in order to conduct the t test in (a)?
C. Construct a boxplot or a normal probability plot to evaluate the assumption made in (b).
D. Do you think that the assumption needed in order to
9.23
A manufacturer of chocolate candies uses machines to package candies as they move along a filling line. Although the packages are labeled as 8 ounces, the company wants the packages to contain a mean of 8.17 ounces so that virtually none of the packages contain less than 8 ounces. A sample of 50 packages is selected periodically, and the packaging process is stopped if there is evidence that the mean amount packaged is different from 8.17 ounces. Suppose that in a particular of 50 packages, the mean amount dispensed is 8.159 ounces, with a sample standard deviation of 0.051
A. Is there evidence that the population mean amount is different from 8.17 ounces? (Use a 0.05 level of significance.)
B. Determine the p-value and interpret its meaning.
9.27
In New York State, savings banks are permitted to sell a form of life insurance called savings bank life insurance (SLBI). The approval process consists of underwriting, which includes a review of the application, a medical information bureau check, possible requests for additional medical information and medical exams, and a policy complication stage in which the policy pages are generated and sent to the bank for delivery. The ability to deliver approved policies to customers in a timely manner is critical to the profitability of this service. During a period of one month, a random sample of 27 approved policies is selected, and the total processing time, in days, is recorded (and stored in insurance):
73
19
16
64
28
28
31
90
60
56
31
56 22 18
45
48
17
17
17
91
92
63
50
51
69
16 17
A. In the past, the mean processing time was 45 days. At the 0.05 level of significance, is there evidence that the mean processing time had changed from 45 days?
B. What assumption about the population distribution is needed in order to conduct the t test in (a)?
C. Construct a boxplot or a normal probability plot to evaluate the assumption made in (b).
D. Do you think that the assumption needed in order to