Question

53,208

23,436

55,459

15,015

15,300

16,100

31,591

27,361

Using the data set above, the mean is 17,548 and the standard deviation is 13,897.

p=.6 and q=.4.

Using the data set above determine the following: A town official claims that the average vehicle in their area sells for more than the 40th percentile of your data set. Run a hypothesis test to determine if the claim can be supported. Please state all the important values.

First determine if you are using a z or t-test and explain why. Then conduct a four-step hypothesis test including a sentence at the end justifying the support or lack of support for the claim and why you made that choice.

Answer 1

This is a z-test because we are comparing the population proportion to a sample proportion.

The hypothesis being tested is:

H₀: p = 0.40

H_a: p > 0.40

The test statistic, z = (p̂ - p)/√p(1-p)/n

z = (0.6 - 0.40)/√0.40(1-0.40)/8

z = 1.15

The p-value is 0.1241.

Since the p-value (0.1241) is greater than the significance level (0.05), we fail to reject the null hypothesis.

Therefore, we cannot conclude that the average vehicle in their area sells for more than the 40th percentile.