Question

For a certain survey, software reports the results shown below for responses on the number of times a week the subject reads a newspaper. Complete parts a through d. Variable N Mean Std Dev SE Mean 95.0% CI News 70 4.4 3.1 0.371 (3.660,5.140) a. Is it plausible that u = 7, where u is the population mean for all respondents? Explain. A. No, because 7 is within the 95% confidence interval given in the software results. B. Yes, because 7 is well outside the 95% confidence interval given in the software results. C. No, because 7 is well outside the 95% confidence interval given in the software results. D. Yes, because 7 is within the 95% confidence interval given in the software results. b. Suppose that the sample size had been 240, with x = 4.4 and s = 3.1. Use technology to find a 95% confidence interval. Describe the effect of sample size on the margin of error. The 95% confidence interval is (I). (Round to one decimal place as needed.)

Answer 1

Solution:

Part b)

Given:

n = 240

T = 4.4

s = 3.1

confidence level = c = 95%

Use following steps in TI 84 plus calculator:

Press STAT and select TESTS

Under TESTS select T-Interval.

Under T interval ,select Stats

Under Stats enter number:

TI-84 Plus Silver Edition TEXAS INSTRUMENTS TInterval Inpt: Data Stats X:4.4 SX:3.1 n: 240 C-Level:.95 Calculate STAT PLOTF1 TBLSETF2 FORMAT F3 CALC F4 TABLE F5 WINDOW ZOOM TRACE GRAPH Y- 2ND ADOR ALPHA TESTA MATH QUI INS MODE DEL LIST STAT ANGLEB DRAW APPS PRGM X.T.en DISTR VARS CLEAR H

Click on Calculate and press Enter

TI-84 Plus Silver Edition TEXAS INSTRUMENTS TInterval (4.0658, 4.7942) X=4.4 Sx=3.1 n=240 STAT PLOTF1 TBLSETF2 FORMAT F3 CALC F4 TABLE F5 Y- WINDOW ZOOM TRACE GRAPH 2ND QUIT MODE INS DEL LIST STAT ALPHA LINK X.T.en TEST A

( 4.0058 , 4.7942)

Round answer to one decimal places, we get:

(4.0 , 4.8)

thus

A 95% confidence interval is: ( 4.0 , 4.8 ).