An auto manufacturer claims that its new 4-cylinder Hybrid auto with manual shift averages 50 mpg under city driving conditions. A Federal Agency believes this claim is too high and decides to randomly test 25 of the manufacturer's 4-cylinder Hybrid autos with manual shift. The Agency determines the mean average mpg for the sample to be 48 with a sample standard deviation of 4 mpg under city driving conditions. The decision rule for this hypothesis test at a = 5% is: a. Reject Ho if the test statistic is greater than 1.65. D. Reject Ho if the test statistic is less than -1.96 or greater than 1.96. C. Reject Ho if the test statistic is less than -1.65. d. Reject Ho if the test statistic is less than -2.33. e. Reject Ho if the test statistic is less than -1.71.
An auto manufacturer claims that its new 4-cylinder Hybrid auto with manual shift averages 50 mpg under city driving conditions. A Federal Agency believes this claim is too high and decides to randomly test 25 of the manufacturer's 4-cylinder Hybrid autos with manual shift. The Agency determines the mean average mpg for the sample to be 48 with a sample standard deviation of 4 mpg under city driving conditions. The decision rule for this hypothesis test at a = 5% is: a. Reject Ho if the test statistic is greater than 1.65. D. Reject Ho if the test statistic is less than -1.96 or greater than 1.96. C. Reject Ho if the test statistic is less than -1.65. d. Reject Ho if the test statistic is less than -2.33. e. Reject Ho if the test statistic is less than -1.71.
Calculus For The Life Sciences
2nd Edition
ISBN:9780321964038
Author:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.
Publisher:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.
Chapter13: Probability And Calculus
Section13.2: Expected Value And Variance Of Continuous Random Variables
Problem 10E
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Transcribed Image Text:An auto manufacturer claims that its new 4-cylinder Hybrid auto with manual shift averages 50 mpg under city driving conditions.
A Federal Agency believes this claim is too high and decides to randomly test 25 of the manufacturer's 4-cylinder Hybrid autos with manual shift.
The Agency determines the mean average mpg for the sample to be 48 with a sample standard deviation of 4 mpg under city driving conditions.
The decision rule for this hypothesis test at a = 5% is:
a.
Reject Ho if the test statistic is greater than 1.65.
D. Reject Ho if the test statistic is less than -1.96 or greater than 1.96.
C.
Reject Ho if the test statistic is less than -1.65.
d.
Reject Ho if the test statistic is less than -2.33.
e.
Reject Ho if the test statistic is less than -1.71.
Expert Solution
Step 1
Decision rule:
Decision rule based on critical value approach:
If test statistic ≤ –t critical value (= –t(α/2)) (or) test statistic ≥ t critical value (=t(α/2)), then reject the null hypothesis H0.
If – t critical value < test statistic < t critical value, then fail to reject the null hypothesis H0.
Step 2
It is given that α = 0.05.
α/2 = 0.05/2=0.025
1-α/2 = 1-0.025 = 0.975.
Find the area 0.975 in the body of the standard normal table.
The critical value is 1.96.
We reject H0 if the test statistic is less than -1.96 or if the test statistic is greater than 1.96.
Correct answer is option (c).
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