2) A 95% confidence interval for the mean difference in ages of houses in the tw

Question

2) A 95% confidence interval for the mean difference in ages of houses in the two neighborhoods was (1.30,20.70). Is this result different than the result of thepooled-t confidence interval? Explain why or why not. Choose the correct answer below.

  A. No. Since the standard deviations are fairly close, the two methods will result in essentially the same confidence intervals and hypothesis tests.

   B. Yes. Since the means are fairly close, the two methods will result in essentially the same confidence intervals and hypothesis tests.

C. Yes. Since the standard deviations are fairly close, the two methods will result in essentially the same confidence intervals and hypothesis tests.

D. No. Since the means are fairly close, the two methods will result in essentially the same confidence intervals and hypothesis tests.

A developer wants to know if the houses in two different neighborhoods were built at roughly the same time. She takes a random sample of six houses from each neighborhood and finds their ages from local records. The accompanying table shows the data for each sample (in years). Assume that the data come from a distribution that is Normally distributed. Complete parts a through c below. Click the icon to view the data table. a) Find a 95% confidence interval for the mean difference, 1-H2, in ages of houses in the two neighborhoods. (Round to two decimal places as needed.) Data Table Neighborhood 1 62 50 49 68 57 Neighborhood 2 A3 47 40 51 50 Print Done

Explanation / Answer

The Mean and standard deviation of both neighbourhood is given below.

Mean of Neighbourhood 1 (x1)= 55

Stadnard deviation of neighbourhood 1 (s1)= 8.99

Mean of neighbourhood 2 (x2)= 44

Standard deviation of neighbourhood 2 (s2) = 6.81

Pooled standard deviation sp = sqrt [(s21 + s22 )/ 2] = 7.975

95% confidence interval for the population mean = (1 - 2 ) +- t10,0.05 sp sqrt (1/ n1 + 1/n2)

= (55 - 44) +- 2.228 * 7.975 * sqrt (1/6 + 1/6)

= 11 +- 2.228 * 7.975 * 0.57735

= (0.74, 21.26)

Queestion 2.

Is this result different than the result of thepooled-t confidence interval?

Yes, the result is different than the result of the pooled t - confidence interval.

The correct answer:

Yes. Since the standard deviations are fairly close, the two methods will result in essentially the same confidence intervals and hypothesis tests. Option C is correct.

Neighbourhood 1 Neighbourhood 2 62 43 50 47 49 40 68 33 57 51 44 50 Average 55 44 Std. Dev. 8.99 6.81

Related Questions

Navigate

• Browse (All)
• Browse 2
• Subjects

---

---

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.