Question

Confidence Intervals 9. Construct a 95 % confidence interval for the population mean, . In a random sample of 32 computers, the mean repair cost was $143 with a sample standard deviation of $35 (Section 6.2) Margin of error, E. <με. Confidence Interval: O Suppose you did some research on repair costs for computers and found that the population standard deviation, a,- $35. Use the normal distribution to construct a 95% confidence interval the population mean, u. Compare the results. Margin of error, E. Confidence Interval: Which confidence interval is wider? 10. Confidence Intervals Repeat Problem 9 using a sample size of 1,000. (Sections 6.1 & 6.2) Mean repair cost $143, s $35 Confidence Interval: Margin of error, E. O $143, a 35. Mean repair cost o Margin of error, E. Confidence Interval: Which confidence interval is wider? Confidence Interval Comparison when sample size is 32 and 1,000 Use the information in problems 9 and 10 Which confidence interval is wider? O o Compare the width differential when the sample size is 1,000 with the width differential when the sample size is 35 (in problem $? What can you conclude about the Normal and t-distributions as the sample sizes increase?

Answer 1

by the problem. tammstag gistribution n=32 I Margin of errra e x met 35 x 2.0395 ~ 39 S = 35. & level of significance lo.gr -0.05. 005; 32-1 from table ~ 12062 cool Tato.025;31 I a 2.6395. confidence interval XE <ML TE 1. 143 - 12.624 H 143 +12.62 • 130.38 < < 155.62 - 1 me me Normal LO 35 n 35.4 x 20.025.1 √32 from 2 table 6.1981.96 - ~ 12.13

Confidence internal - % E M L XtE 143-12.13.2 M2 143 + 12.13 30-87 LM L 155.13 28 in care of Confidence 1 is internal wider. anton 10 Desa Naw na 16oo. x=143 3:35 ... S x tahan na Cast 35 * 2.0395 J1ooo 226. det D Confidence internal - ☆ - E CML ÅTE 193-2.26 < < 143+2.26 140.74 SM s 145.26.

% = 1430 235 2.13 & 2 o y Zala roo V 35x1.96 e riooo ~ 2017 9 Confs dence internal of X-ES M. åte 143-2:12 < M < 143 +2.19. 140.832 M 2 145 • 17. 0 i luleval is wider. 9

inlinale no Sample size 1000 3:35 I I Call 0235 au (IV I in roman width difference in 1st Care 5235 when n = 32 E distributia & na 1000 (1)-(111) mini esnob doros = (155.62 - 130:58) - (145.26-140.74) Cli 2 0.72. 6335 Normal) width diff. En and care. or (55-13 - 130.89) - (195.12 - 140.83) 19.92 as and the confidence ineival narrows down in both Normal & t distribution Nole - na e sample sizes increases.