Question

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Question 20 1 pts A consumer group plans to test whether a car gets at least 28 MPG. They will test the hypothesis using a significance level of 0.05 and a sample size of n = 121 cars. Assume the population standard deviation is 6 mpg. Based on this information, what is the critical value in terms of miles per gallon? © 27.1028 C Can't be determined without more information © 28.8601 C 26.3582

Answer 1

Solution:

Thu null and alternative hypothesis are

H₀; $\mu$ $\geq$ 28 vs H_a: $\mu$ < 28

Left tailed test

$\alpha$ = 0.05

Critical value is $-z_{\alpha}$ = $-z_{0.05}$ =

The test statistic z is given by

z = $\frac{\bar x - \mu0}{\sigma/\sqrt{n}}$

At critical value , $-z_{\alpha}$ = -1.645 , find the value of $\bar x$

-1.645 = [$\bar x$ - 28]/[6/$\sqrt{}$121]

Solving we get

$\bar x$ = 27.1028

Answer : 27.1028