Stephanie believes that the average running time of movies is equal to 140 minut

Question

Stephanie believes that the average running time of movies is equal to 140 minutes. A sample of 4 movies was taken and the following running times were obtained. Assume the distribution of the population is normally distributed.

150

150

180

170

a.

State the null and alternative hypotheses.

b.

Using a critical value, test the hypothesis at the 10% level of significance.

c.

Using a p-value, test the hypothesis at the 10% level of significance.

d.

Using a confidence interval, test the hypothesis at the 10% level of significance.

e.

Could a Type II error have been committed in this hypothesis test?

150

150

180

170

Explanation / Answer

Null Hypothesis = H0 = 140 i.e average running time of movies is equal to 140 minutes

Alternative Hypothesis = H1 = average running time of movies is not equal to 140 minutes i.e H1> 140 or H1< 140

Avg(x) = (150+150+180+170)/4 = 162.5

Population mean(m) = 140

n= 4

Standard deviation = 15

t test = (x-m)/(s/sqrt(n))

= (162.5-140)/ (15/sqrt 4)

=(162.5-140)/7.5

=3 (calculated value)

critical value = n-1

= 4-1

=3

level of sig =.10

so tabulated t at (1-0.10 and 3) = 1.638

since our calculated value is higher than tabulated value null hyp is rejected

critical value = 1-0.10 = .90

No, type 2 error cannot be committed because null hypothesis at type1 is rejected. A Type II error occurs when the researcher accepts a null hypothesis that is false.

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