The Fast Motor Company wishes to estimate the mean dollar amount of damage done

Question

The Fast Motor Company wishes to estimate the mean dollar amount of damage done to a new model speedster as a result of a 10 mph crash into the rear bumper of a parked car. 36 Speedsters are test crashed into parked cars and the dollar amount of damage done to each is recorded. The result from the sample are x = $438 and s= $86.
Conduct a hypothesis test. What is the p-value and how much evidence is there that the population mean damage is less than $475, i.e, to reject the null hypothesis Ho: u> $475 and accept the alternative hypothesis Ha: u< $475?

Answer:
p-value, and round your answer to three decimal places.
The weight of evidence in support of the alternative hypothesis that the population mean damage is less than $475 is?

Explanation / Answer

The test hypothesis is
Ho: u> $475
Ha: u< $475

The test statistic is
Z=(xbar - u)/(s/n)

=(438-475)/(86/sqrt(36))

= -2.58

The p-value is

P(Z< -2.58) = 0.0049 (check standard normal table)

Since p-value= 0.0049 is very small, we reject Ho. So we can conclude that population mean damage is less than $475

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