Before changes to its management staff, an automobile assembly line operation had a scheduled mean completion time of 15 minutes. The standard deviation of completion times was 1.4 minutes. An analyst at the company suspects that, under new management, the mean completion time, μ, is now less than 15 minutes. To test this claim, a random sample of 20 completion times under new management was taken by the analyst. The sample had a mean of 14.2 minutes. Assume that the population is normally distributed. Can we support, at the 0.05 level of significance, the claim that the population mean completion time under new management is less than 15 minutes? Assume that the population standard deviation of completion times has not changed under new management. Perform a one-tailed test. Then complete the parts below. Carry your intermediate computations to three or more decimal places, and round your responses as specified below. (If necessary, consult a list of formulas.) (a) State the null hypothesis Ho and the alternative hypothesis H₁. (b) Determine the type of test statistic to use. (Choose one) ▼ (c) Find the value of the test statistic. (Round to three or more decimal places.) 0 (d) Find the p-value. (Round to three or more decimal places.) (e) Can we support the claim that the population mean completion time under new management is less than 15 minutes? O Yes O No μ X 84 0=0 O X S ê 2 00 OSO P 00 020 0#0 O0 Ś
Before changes to its management staff, an automobile assembly line operation had a scheduled mean completion time of 15 minutes. The standard deviation of completion times was 1.4 minutes. An analyst at the company suspects that, under new management, the mean completion time, μ, is now less than 15 minutes. To test this claim, a random sample of 20 completion times under new management was taken by the analyst. The sample had a mean of 14.2 minutes. Assume that the population is normally distributed. Can we support, at the 0.05 level of significance, the claim that the population mean completion time under new management is less than 15 minutes? Assume that the population standard deviation of completion times has not changed under new management. Perform a one-tailed test. Then complete the parts below. Carry your intermediate computations to three or more decimal places, and round your responses as specified below. (If necessary, consult a list of formulas.) (a) State the null hypothesis Ho and the alternative hypothesis H₁. (b) Determine the type of test statistic to use. (Choose one) ▼ (c) Find the value of the test statistic. (Round to three or more decimal places.) 0 (d) Find the p-value. (Round to three or more decimal places.) (e) Can we support the claim that the population mean completion time under new management is less than 15 minutes? O Yes O No μ X 84 0=0 O X S ê 2 00 OSO P 00 020 0#0 O0 Ś
Glencoe Algebra 1, Student Edition, 9780079039897, 0079039898, 2018
18th Edition
ISBN:9780079039897
Author:Carter
Publisher:Carter
Chapter10: Statistics
Section10.6: Summarizing Categorical Data
Problem 31PPS
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Transcribed Image Text:Before changes to its management staff, an automobile assembly line operation had a scheduled mean completion time of 15 minutes. The standard deviation of
completion times was 1.4 minutes. An analyst at the company suspects that, under new management, the mean completion time, μ, is now less than 15
minutes. To test this claim, a random sample of 20 completion times under new management was taken by the analyst. The sample had a mean of 14.2
minutes. Assume that the population is normally distributed. Can we support, at the 0.05 level of significance, the claim that the population mean completion
time under new management is less than 15 minutes? Assume that the population standard deviation of completion times has not changed under new
management.
Perform a one-tailed test. Then complete the parts below.
Carry your intermediate computations to three or more decimal places, and round your responses as specified below. (If necessary, consult a list of formulas.)
(a) State the null hypothesis Ho and the alternative hypothesis H₁.
HO
H₁ :0
(b) Determine the type of test statistic to use.
(Choose one) ▼
(c) Find the value of the test statistic. (Round to three or more decimal places.)
0
(d) Find the p-value. (Round to three or more decimal places.)
0
(e) Can we support the claim that the population mean completion time under
new management is less than 15 minutes?
OYes O No
H
|x
5
a
S
X
00
Р
<Q
010
ロ=ロ OSO 020
0#0 O<O ☐>0
S
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