3a . Summary statistics for Importance_Internet_access: Group by: Gender Gender

Question

3a.

Summary statistics for Importance_Internet_access:
Group by: Gender

Gender

n

Mean

Std. dev.

Female

238

681.90

341.39

Male

191

713.993

317.148

  

3b. Use the information from part 3a to construct a 95% confidence interval ‘by-hand’ for the difference between the means for males and females (males-females) on the variable Importance_Internet_access. Show all work and the formula. Note: Use t*=1.96 as both sample sizes are so large. Report your confidence interval in both formats: statistic +/- margin for error and (lower limit, upper limit) rounded to two decimal places.

3c.

Two sample T confidence interval:
1 : Mean of Importance_Internet_access where Gender=Male
2 : Mean of Importance_Internet_access where Gender=Female
1 - 2 : Difference between two means
(with pooled variances)

95% confidence interval results:

Difference

Sample Diff.

Std. Err.

DF

L. Limit

U. Limit

1 - 2

32.086167

32.137686

427

-31.081584

95.253918

3d. In a complete sentence, interpret the confidence interval results from part 3c in the context of the question.

3e. Use your confidence interval results from part 3c to determine if you should reject or fail to reject the null hypothesis if you had decided to conduct a two-sided hypothesis test instead of creating a confidence interval to determine if there was a difference in the means for males and females for the variable Importance_Internet_access. Justify your decision in a sentence using your confidence interval.

Gender

n

Mean

Std. dev.

Female

238

681.90

341.39

Male

191

713.993

317.148

Explanation / Answer

Question 3b

Confidence interval = (X1bar – X2bar) -/+ t*sqrt((S1^2/n1)+(S2^2/n2))

Confidence interval = (713.993 - 681.90) -/+ 1.96*sqrt((317.148^2/191)+(341.39^2/238))

Confidence interval = 32.093 -/+ 62.48392

Lower limit = 32.093 - 62.48392 = -30.3909

Upper limit = 32.093 + 62.48392 = 94.57692

Confidence interval = (-30.3909, 94.57692)

Question 3d

We are 95% confident that the population average difference between two means for male and female would be lies between -31.081584 and 95.253918.

Question 3e

Here, we have to use two sided two sample t test for difference between two population means.

H0: µ1 - µ2 = 0 versus Ha: µ1 - µ2 0

Test statistic = t = (X1bar – X2bar)/ sqrt((S1^2/n1)+(S2^2/n2))

Test statistic = t = 32.086167/ 32.137686 = 0.998397

Critical value = 1.96

Test statistic value < Critical value

So, we do not reject the null hypothesis H0: µ1 - µ2 = 0

There is sufficient evidence to conclude that there is no significant difference in population means.

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