Question

Data: Pets owned by men: 1, 2, 3, Pets owner by women: 0, 0, 0, 0, 1, 2, 3, 3

Questions:

1a. How many pets do the men in the class own? Write down each data point.

2. What is the mean number of pets the men in class own?

2a. What is the standard deviation of the number of pets the men in class own? You can use Excel for this computation.

3. How many pets do the women in the class own? Write down each data point.

3a. What is the mean number of pets the women in class own?

4. What is the standard deviation of the number of pets the women in class own?

4a. Use the formulas in class to give a 90% confidence interval for the difference in the mean number of pets men own and the mean number of pets women own.

4b.Do men and women seem to differ in the number of pets they own? Explain.

4c. We want to do a hypothesis test to see if men and women differ in pet ownership. 17. What are the hypotheses?

5. Use the formulas provided in class to compute the t-score.

5a. Find the P-value.

5b. Interpret your results in the context of the research question.

5c. Do the results from the confidence interval and hypothesis test agree or disagree? Explain.

Answer 1

S.N.	Pet own by
	Men	Women
1	1	0
2	2	0
3	3	0
4		0
5		1
6		2
7		3
8		3
Total	6	9
Average	2	1.125
Variance	0.666667	1.609375
Standard deviation	0.816497	1.268611

Two-Sample T-Test and CI: Pet own by men, Pet own by women

Method

μ₁: mean of Pet own by men

µ₂: mean of Pet own by women

Difference: μ₁ - µ₂

Equal variances are not assumed for this analysis.

Descriptive Statistics

Sample	N	Mean	StDev	SE Mean
Pet own by men	3	2.00	1.00	0.58
Pet own by women	8	1.13	1.36	0.48

Estimation for Difference

Difference	90% CI for Difference
0.875	(-0.637, 2.387)

Test

Null hypothesis	H₀: μ₁ - µ₂ = 0
Alternative hypothesis	H₁: μ₁ - µ₂ ≠ 0

T-Value	DF	P-Value
1.17	5	0.296

1a. How many pets do the men in the class own? Write down each data point.

= 1 + 2 + 3

= 6

2. What is the mean number of pets the men in class own?

= 2 pets.

2a. What is the standard deviation of the number of pets the men in class own?

= 0.816497

3. How many pets do the women in the class own ?

= 0 + 0 + 0 + 0 + 1 + 2 + 3 + 3

= 9 Pets.

3a. What is the mean number of pets the women in class own?

= 1.125 pets.

4. What is the standard deviation of the number of pets the women in class own?

= 1.268611 pets.

4a. Use the formulas in class to give a 90% confidence interval for the difference in the mean number of pets men own and the mean number of pets women own.

= (-0.637, 2.387)

4b.Do men and women seem to differ in the number of pets they own?

= Since the zero is included in the confidence interval, men and women don't seem to differ in the number of pets they own.

4c. We want to do a hypothesis test to see if men and women differ in pet ownership. 17. What are the hypotheses?

Null hypothesis	H₀: μ₁ - µ₂ = 0
Alternative hypothesis	H₁: μ₁ - µ₂ ≠ 0

where,

μ₁: mean of Pet own by men

µ₂: mean of Pet own by women

Difference: μ₁ - µ₂

5. Use the formulas provided in class to compute the t-score.

= { (xbar1 - xbar2) / Sq. root [ (S1^2)/n1 + (S2^2)/n2 ]

= 1.17

5a. Find the P-value.

= 0.296

5b. Interpret your results in the context of the research question.

= Since the p-value is greater than the level of significance, we can't reject the null hypothesis at 10% level of significance.

Hence the men and women don't seem to differ in the number of pets they own.

5c. Do the results from the confidence interval and hypothesis test agree or disagree? Explain.

Since both method reject the null hypothesis, the result from the confidence interval and hypothesis test agree.