The null and alternate hypotheses are: H0 : μ1 = μ2H1 : μ1 ≠ μ2 A random sample of 9 observations from one population revealed a sample mean of 25 and a sample standard deviation of 4.0. A random sample of 4 observations from another population revealed a sample mean of 29 and a sample standard deviation of 4.6. At the 0.01 significance level, is there a difference between the population means? a) State the decision rule. (Negative amounts should be indicated by a minus sign. Round your answers to 3 decimal places.) The decision rule is to reject H0 if t <______ or t>_______ b) Compute the pooled estimate of the population variance. (Round your answer to 3 decimal places.) c) Compute the test statistic.(Negative amount should be indicated by a minus sign. Round your answer to 3 decimal places.)

A researcher is interested in seeing if the average income of rural families is greater than that of urban families. To see if his claim is correct he randomly selects 33 families from a rural area and finds that they have an average income of $67042 with a population standard deviation of $504. He then selects 55 families from a urban area and finds that they have an average income of $65999 with a population standard deviation of $770. Perform a hypothesis test using a significance level of 0.05 to test his claim. Let rural families be sample 1 and urban familis be sample 2. The correct hypotheses are: HA: H > H2 1„(claim) Ho : 41 2 H2 (claim) > It : 'H H, : H1 = H2 4„(claim) Since the level of significance is 0.05 the critical value is 1.045 The test statistic is (round to 3 places) The pvalue is: (round to 3 places) The decision can be made to: reject H, do not reject H, The final conclusion is that: There is enough evidence to reject the claim that the average income of rural…

Suppose we are contracted by the Justice Department to study the extent of juvenile delinquency.  We take a random sample of 100 juveniles, and we find that the mean number of crimes committed is 12 with a standard deviation of 7. Test the null hypothesis that the mean number of crimes committed by the population of juveniles is less than or equal to 11.  Use a significance level of .05.  (Be sure to show the numeric results that lead to your decision.)  Do we reject the null hypothesis here? why or why not.

A random sample of 43 subjects who identified themselves as compulsive buyers was obtained and given a questionnaire. They had a mean questionnaire score of 0.52 with a standard deviation of 0.17. Test the claim that the population of self-identified compulsive buyers has a mean greater than the mean of 0.51 for the general population. Use a 0.05 significance level. State the null and alternative hypotheses. O B. Ho H= 0.51 O A. H, p= 0.51 H3 p> 0.51 H3 µ#0.51 ОС. Но н0.51 H3 p= 0.51 O D. Ho H=051 H, p<0,51