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.

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Description: 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

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MATLAB: An Introduction with Applications

6th Edition

ISBN:9781119256830

Author:Amos Gilat

Publisher:Amos Gilat

Chapter1: Starting With Matlab

Section: Chapter Questions

Problem 1P

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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 H_0.

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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