Question

9. The average number of cars per household in the year 2000 is known to have been 1.97. A researcher believes that the average has increased by the year 2018. In 2018 he 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) b. [4 pts] Perform the appropriate hypothesis test and produce relevant values (i.e., p- value and test statistics) c. [3 pts] Write a statement describing the result of your analysis and the conclusion.

Answer 1

1.97 (there is no significant increase) 1.97 (there is significant increase) 2.05 n= 155 S= 0.58 154 Null hypothesis;HO: us Alternative hypothesis;H1 H1> sample mean: x = Sample size : Sample s.d : Degrees of freedom: n-1 = Level of significance : a = Critical value: Decision rule : Reject HO if t> Test statistic: X- 0.05 a 1.655 1.655 t = 1.7171 S p-value: Fort = 1.717 with df= 154 The right tailed p-value is 0.0440 Decision : Since p-value <a ,reject HO Conclusion : There is sufficient evidence to support the belief that the average has increased.