Question

Sample5(ACTRESSES)	Sample5(ACTORS)
38	37
45	43
25	42
28	43
40	44
22	41
35	56
34	44
24	47
33	29
33	31
26	37
32	34
21	32
29	51
33	42
26	60
41	32
54	52
43	39
54	54
35	45
35	34
27	47
35	60
29	37
29	53
35	60
31	33
30	38

1. The sample you were given in class comes from Data Set 14 “Oscar Winner Age” in your textbook. They are the ages of winners of the Best Actress and Best Actor for the Oscars. Below, please record the sample statistics below and then use them to answer the questions that follow. If you did not receive a sample, please email your instructor for a data set.

                Sample number                                

	Best Actress	Best Actor
Sample mean
Sample Standard Deviation
Sample size
Min
First Quartile
Med
Second Quartile
Max

2. Using the data above based on your samples of Best Actress and Best Actor winners, compute a 95% confidence interval for mean age μ of the Best Actor winners and determine the margin of error.

               

3. Using the data calculated on page 1 based on your sample of Best Actress winners, test the claim at α = 0.05 significance level that the mean age of Best Actress winners is greater than 40.
   1. State the null hypothesis and alternative hypothesis.

                                H₀:                                                         

                                H₁:                                                         

2. Determine the test statistic and the P‐Value

                                Test Statistic:                                                                    

                                P‐Value:                                                                              

3. Make a decision about the null hypothesis. Briefly justify your answer.
4. Write a conclusion that incorporates the original claim directly.

Answer 1

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	Best Actress	Best Actor
Sample mean	33.40	43.23
Sample Standard Deviation	8.12	9.17
Sample size	30	30
Min	21	29
First Quartile	28.25	37.00
Med	33	42.5
Second Quartile	33	42.5
Max	54	60

................................................................................................................................................................

Using Excel<data<megastat<hypotheis test<paired t test

Here is the output:

Hypothesis Test: Paired Observations
	0.000	hypothesized value
	33.400	mean Sample5(ACTRESSES)
	43.233	mean Sample5(ACTORS)
	-9.833	mean difference (Sample5(ACTRESSES) - Sample5(ACTORS))
	11.161	std. dev.
	2.038	std. error
	30	n
	29	df
	-4.826	t
	4.12E-05	p-value (two-tailed)
	-14.001	confidence interval 95.% lower
	-5.666	confidence interval 95.% upper
	4.167	margin of error

Using the data above based on your samples of Best Actress and Best Actor winners, compute a 95% confidence interval for mean age μ of the Best Actor winners and determine the margin of error.

Confidence interval (-14.001,-5.666)

Lower limit -14.001

Upper limit -5.666

Margin of Error= 4.167

......................................................................................................................................................................................

Using Excel data<megastat<hypothesis test<mean

Hypothesis Test: Mean vs. Hypothesized Value
	40.000	hypothesized value
	33.400	mean 1
	8.120	std. dev.
	1.483	std. error
	30	n
	29	df
	-4.452	t
	.9999	p-value (one-tailed, upper)
	30.368	confidence interval 95.% lower
	36.432	confidence interval 95.% upper
	3.032	margin of error

1. Using the data calculated on page 1 based on your sample of Best Actress winners, test the claim at α = 0.05 significance level that the mean age of Best Actress winners is greater than 40.

From above we get x bar= 33.4 , n=30, standard deviation= 8.12

1. State the null hypothesis and alternative hypothesis.

                                H0:u=40

                                H1: u>40

1. Determine the test statistic and the P‐Value

                                Test Statistic: -4.452   

                                P‐Value: 0.9999

1. Make a decision about the null hypothesis. Briefly justify your answer.

Since P value=0.9999>alpha(0.05). We fail to reject the null hypothesis.

1. Write a conclusion that incorporates the original claim directly.

There is not sufficient evidence to conclude that the mean age of Best Actress winners is greater than 40.