Question

A researcher believes that the average has increased by the year 2018. In 2018 he 9. The average number of cars per household in the year 2000 is known to have been 1.97. surveys 155 households, and finds that for this sample, the mean is 2.05 with a standard deviation of .58 I would like you to test the researcher's belief statistically at the a= .05 level of significance. a. [3 pts) State the Null and Alternative hypotheses (in symbols and words) Ho Hall & 1.97 - 197 b. [4 pts) Perform the appropriate hypothesis test and produce relevant values (i.e.,p- value and test statistics) Pvalue = 0.0879 t-stat = 167172 c. [3 pts] Write a statement describing the result of your analysis and the conclusion. d. [3 pts) What happens if you test the hypothesis at the a=.01 level of significance? i.e., Does the conclusion change? Why or why not?

can you help me to resolve this.. please I'm stuck..

Answer 1

solution Given the internation u= average oumbeo cf 1985.7.97 n=155 X-level of significanco=0:05 = samoh mean - 2005 3 sample standard deviation = 10:58 the claim that a peer researcher believe that the overage has increased by the year 2018 vull bypothegis - Average number of cuds per household. is 1.97 70 test VS Alternative hypothesis → Ayerage number of cuts per yeud is not equal to 177. i-e. Hoiu: 197 Hei 4 £1.97 6 The formula for the test statisticis, t = x-t son 2.05-1.97 0.58/VISS 7-statistic-.7172 We obtain the p-value is excel by using the command -xalue - 70231 C test statistic, difteril) dit: degule of freedom ne) def. =155-1= 154 for one failed test tail For two-tailed test Here H, is not equal to type so test is fue_1100-teiled test

- : P-value = 70257667/72,1542) 0.087853 But test is two tailed test 2*0:08 +953 = 0.175906 P-value = 0.1759 (Round to a decimal ilave piare Decision Belle using puralue method Reject to when p-value is less than og equal to lever of signi ficance feeil to fr reject otheowise - 0.1759 20:05 Feell to reject Ho at 5% level of siguificance conclusion that there is insufficient exidence to support the claim the aresage has increased by the year 2018 at 5 % level of Significance he say