Determine the 95% confidence interval for the difference between two population means where sample 1 has...

Determine the 95% confidence interval for the difference between two population means where sample 1 has data: 16, 14, 19, 18, 19, 20, 15, 18, 17, 18, and sample 2 has data: 13, 19, 14, 17, 21, 14, 15, 10, 13, 15. (Assume equal population variances)

Solutions

Expert Solution

	sample 1 ( X )	Σ ( X_i- X̅ )²	Sample 2 ( Y )	Σ ( Y_i- Y̅ )²
	16	1.96	13	4.41
	14	11.56	19	15.21
	19	2.56	14	1.21
	18	0.36	17	3.61
	19	2.56	21	34.81
	20	6.76	14	1.21
	15	5.76	15	0.01
	18	0.36	10	26.01
	17	0.16	13	4.41
	18	0.36	15	0.01
Total	174	32.4	151	90.9

Mean X̅ = Σ Xi / n
X̅ = 174 / 10 = 17.4
Sample Standard deviation S_X = √ ( (Xi - X̅ )2 / n - 1 )
S_X = √ ( 32.4 / 10 -1 ) = 1.8974

Mean Y̅ = ΣYi / n
Y̅ = 151 / 10 = 15.1
Sample Standard deviation S_Y = √ ( (Yi - Y̅ )2 / n - 1 )
S_Y = √ ( 90.9 / 10 -1) = 3.178

Confidence interval is :-
( X̅1 - X̅2 ) ± t( α/2 , n1+n2-2) SP √( (1/n1) + (1/n2))

t(α/2, n1 + n1 - 2) = t( 0.05/2, 10 + 10 - 2) = 2.101
( 17.4 - 15.1 ) ± t(0.05/2 , 10 + 10 -2) 2.6172 √ ( (1/10) + (1/10))
Lower Limit = ( 17.4 - 15.1 ) - t(0.05/2 , 10 + 10 -2) 2.6172 √( (1/10) + (1/10))
Lower Limit = -0.159
Upper Limit = ( 17.4 - 15.1 ) + t(0.05/2 , 10 + 10 -2) 2.6172 √( (1/10) + (1/10))
Upper Limit = 4.759
95% Confidence Interval is ( -0.159 , 4.759 )

orchestra answered 1 year ago

Next > < Previous

Related Solutions

In constructing 95% confidence interval estimate for the difference between the means of two populations, where...

In constructing 95% confidence interval estimate for the difference between the means of two populations, where the unknown population variances are assumed not to be equal, summary statistics computed from two independent samples are: ?1=45,?̅1=756,?1=18,?2=40,?̅2=762,?2=15 (using 2-sample T menu) a. Calculate the 95% confidence interval for the true difference of two means. b. Base on the interval in the previous question, can one conclude there is a difference in means of two populations? Justify your answer.

Describe a confidence interval for the difference in means between two population by stating 1. a...

Describe a confidence interval for the difference in means between two population by stating 1. a pair of populations composed of the same type of individuals and a quantitative variable on those populations, 2. sizes and degrees of freedom of samples from those populations, 3. the means of those samples, and 4. the standard deviations of those samples. Then state 5. a confidence level and find 6. find the interval. Finally, perform a test of significance concerning the difference in...

1. Confidence interval for the difference between the two population means. (Assume that the two samples...

1. Confidence interval for the difference between the two population means. (Assume that the two samples are independent simple random samples selected from normally distributed populations.) A researcher was interested in comparing the GPAs of students at two different colleges. Independent simple random samples of 8 students from college A and 13 students from college B yielded the following summary statistics: College A College B = 3.1125 = 3.4385 s1 = 0.4357 s2 = 0.5485 n1 = 8 n2 =...

Construct the indicated confidence interval for the difference between the two population means.

Construct the indicated confidence interval for the difference between the two population means. Assume that the two samples are independent simple random samples selected from normally distributed populations. Do not assume that the population standard deviations are equal. Independent samples from two different populations yield the following data. The sample size is 478 for both samples. Find the \(85 \%\) confidence interval for \(\mu_{1}-\mu_{2}\). \(\bar{x}_{1}=958, \bar{x}_{2}=157, s_{1}=77, s_{2}=88\) A. \(800<\mu_{1}-\mu_{2}<802\) B. \(791<\mu_{1}-\mu_{2}<811\) C. \(793<\mu_{1}-\mu_{2}<809\) D. \(781<\mu_{1}-\mu_{2}<821\)

Calculate the 95% confidence interval for the difference (mu1-mu2) of two population means given the following...

Calculate the 95% confidence interval for the difference (mu1-mu2) of two population means given the following sampling results. Population 1: sample size = 14, sample mean = 12.96, sample standard deviation = 1.38. Population 2: sample size = 12, sample mean = 2.55, sample standard deviation = 1.05.

Construct the indicated confidence interval for the difference between the two population means. Assume that the...

Construct the indicated confidence interval for the difference between the two population means. Assume that the two samples are independent simple random samples selected from normally distributed populations. Do not assume that the population standard deviations are equal. A paint manufacturer wished to compare the drying times of two different types of paint. Independent simple random samples of 11 cans of type A and 9 cans of type B were selected and applied to similar surfaces. The drying times, in...

Construct the indicated confidence interval for the difference between the two population means. Assume that the...

Construct the indicated confidence interval for the difference between the two population means. Assume that the two samples are independent simple random samples selected from normally distributed populations. Also assume that the population standard deviations are equal (sigma1 = sigma2), so that the standard error of the difference between means is obtained by pooling the sample variances. A paint manufacturer wanted to compare the drying times of two different types of paint. Independent simple random samples of 11 cans of...

You are trying to estimate the confidence interval for the difference between two population means based...

You are trying to estimate the confidence interval for the difference between two population means based on two independent samples of sizes n1=24 and n2=28. Which option below is NOT relevant for this case? Select one: a. To build the CI we have to obtain the critical value from a t-distribution with appropriate degrees of freedom. b. To build the CI we have to estimate sample means based on each random sample. c. To build the CI we have to...

Compute the confidence interval for the difference of two population means. Show your work. Sample Mean...

Compute the confidence interval for the difference of two population means. Show your work. Sample Mean 1= 17 Population standard deviation 1= 15 n1= 144 Sample Mean 2= 26 Population Standard Deviation 2= 13 n2 = 121 Confidence Level= 99

A 95% confidence interval of ________ means that there is a 95% chance that the population mean falls within the range between 5.1 and 6.1.

T / F 12. A 95% confidence interval of ________ means that there is a 95% chance that the population mean falls within the range between 5.1 and 6.1. T / F 13. Mean is more sensitive to extreme values than median. T / F 14. A sampling distribution describes the distribution of a particular sample characteristic for all possible samples, random or not, of a specific sample size. T / F 15. t-distribution has a higher skewness than...

Subjects