Question

Use the data from problem #1. Assume a probability normal probability plot suggest the data could come from a population that is normally distributed. A boxplot does not show outliers. Does the sample evidence suggest the cost of repairs to exceed $1200? (2 point) What type of test should we use? а. sample -test for the b. (4 points) Write the hypotheses and specify the type of test (tailing). Use appropriate notation for the hypotheses. Hypotheses: Tailing: Calculate (formula/values) the test statistic and the associated p-value range from the table C. (4 points) Test Stat: P-Value: d. (2 point) State the decision of the test, Express your conclusion concisely using statistically appropriate language applied to repair costs. е. (2 points)

Answer 1

Calculations for the mean and standard deviation are given below

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(a) One sample t test for mean.

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(b) The Hypothesis:

H0: $\mu$ = 1200

Ha: $\mu$ > 1200

This is a right tailed (one tailed test)

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(c) The Test Statistic:

t = \frac{\bar{x}-\mu }{\frac{s}{\sqrt{n}}} = \frac{1756.5-1200}{\frac{1007.4542}{\sqrt{10}}} = 1.75

P value = 0.057. Therefore the p value range is 0.05 < p value < 0.10

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(d) Since p value is not mentioned, we use the defualt level = 0.05.

Since p value is > 0.05, Then fail to reject H0.

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(e) The conclusion is that there is insufficient evidence at the 95% significance level to conclude that the average cost of repairs for mini and micro vehicles who have been in a low impact collision is greater than $1200.

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Please note: In case Alpha is 0.10, the the decision would be to reject H0 as p value would be < Alpha.

The conclusion would be that there is sufficient evidence at the 90% significance level to conclude that the average cost of repairs for mini and micro vehicles who have been in a low impact collision is greater than $1200.

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Calculation for the mean and standard deviation:

Mean = Sum of observation / Total Observations

Standard deviation = SQRT(Variance)

Variance = Sum Of Squares (SS) / n - 1, where SS = SUM(X - Mean)².

#	X	Mean	(x - mean)2
1	3148	1756.50	1936272.25
2	1758	1756.50	2.25
3	1071	1756.50	469910.25
4	3345	1756.50	2523332.25
5	743	1756.50	1027182.25
6	2057	1756.50	90300.25
7	663	1756.50	1195742.25
8	2637	1756.50	775280.25
9	773	1756.50	967272.25
10	1370	1756.50	149382.25
Total	17565		9134676.50

n	10
Sum	17565
Average	1756.50
SS(Sum of squares)	9134676.5
Variance = SS/n-1	1014964.056
Std Dev=Sqrt(Variance)	1007.4542