Answer :
Answer with explanation:
Let [tex]\mu[/tex] be the population mean.
For the given claim , we have
Null hypothesis : [tex]H_0: \mu=35.9[/tex]
Alternative hypothesis : [tex]H_a: \mu\neq35.9[/tex]
Since alternative hypothesis is two-tailed , so the test is a two-tailed test.
Given : Sample size : n=220 ;
Sample mean: [tex]\overline{x}=35.6[/tex] ;
Standard deviation: [tex]s=2.2[/tex]
Test statistic for population mean:
[tex]z=\dfrac{\overline{x}-\mu}{\dfrac{s}{\sqrt{n}}}[/tex]
[tex]z=\dfrac{35.6-35.9}{\dfrac{2.2}{\sqrt{220}}}\approx-2.02[/tex]
By using the standard normal distribution table of z , we have
P-value ( two tailed test ) : [tex]2P(Z>|z|)=2(1-P(Z<|z|))[/tex]
[tex]=2(1-P(z<|-2.02|))=2(1-0.9783083)=0.0433834[/tex]
Since , the P-value is greater than the significance level of [tex]\alpha=0.02[/tex] , it means we do not have sufficient evidence to reject the null hypothesis.
Final answer:
The question is looking at hypothesis testing in accordance with the manufacturer's claim of MPG rating. Based on the data, we would likely fail to reject the null hypothesis--i.e., go with the manufacturer's claim--as the difference between the sample mean and the manufacturer's claim is small. However, an explicit conclusion requires performing a Z test.
Explanation:
This question is looking at hypothesis testing of a claimed miles-per-gallon rating. We would define the null hypothesis (H0) as the manufacturer's claim, which is that the MPG rating is 35.9. The alternative hypothesis (Ha) would be that the MPG rating is not 35.9. The sample mean is 35.6 from 220 cars, with a known standard deviation of 2.2. When testing the null hypothesis, we can use the Z test for known standard deviations. If the computed Z score is less than the critical value at a significance level of 0.02, we fail to reject the null hypothesis. Alternatively, if it's greater, we reject the null hypothesis.
Without conducting the actual Z test here, the provided context suggests that the difference between the sample mean and the anticipated population mean is small, it may not be statistically significant, leading us to potentially fail to reject the null hypothesis. This means we could conclude that the manufacturer's MPG rating may not be incorrect. Anyway, without the exact calculations, this cannot be definitively stated.
Learn more about Hypothesis Testing here:
https://brainly.com/question/34171008
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