Question

4. In a sample of 150 heads of households in the U.S.92 reported that they own their own home. Find a 99% confidence interval for the true proportion of the U.S. population that owns their own home The StatCrunch output for a 99% confidence interval is below. Proportion Count Total Sample Prop. Std. Err. L. Limit U. Limit р 92 150 0.61333333 0.039762256 0.51091255 0.71575412 a. Write out the interval and interpret the interval in the context of this problem. Round to 3 decimal places. A recent report stated that 65% of the U.S. population owns their own home. Is the actual percentage less? Test at the 1% level. b. Write the hypotheses in symbols and in words: The StatCrunch output for the hypothesis test is below

Answer 1

The solution to this problem is given by

The given data i's Total Proborden Cound р 99. Sample Pro. Stand Errer 0.6133 0.03976 150 Upper limit lower liniet 0.51091255 0.71575412 ginterpretation (a) We are 99% confident that the true proportion all Use & opulation that owns their own of home will be between 0.5t i and 0.71.6 the

(bl The null and alternative by bother's is Null Hypothesis Ho! 651. of all u.s. population have their own homes 08 Ho: P = 0.65 Alternative Hypothers: Hi The loodulation of U.S. their which have own hom id is les than 654 or Hii P 2065 (C) Since z Spect Zcal =-0,9415 And P-value = 0.1732 At P-value 72, So we fail to Rejet Ha. Do not Reject Ho. (el) Conchesion : Fail to Reject Ho, the data provide insufficient evidence to conclude that less than 65% population of U.so have homes. G 5

( e . Test Statistics 2= d-d Ulog/n 42 150 0.65 = 1.9=14 E|-0-6 0.35 (0.65)(035)150 0.6133 -0.65 = -0.942475603 12 0.03894 Z-Steel 0.942475603