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Practice 11:

Statistical Inference

Question 1

What percentage of the population live in their state of birth?  According to the U.S. Census Bureau’s American Community Survey, the figure ranges from 25% in Nevada to 78.7% in Louisiana. The average percentage across all states and the District of Columbia is 57.7%. The data in the file HomeState are consistent with the findings in the American Community Survey. The data are for a random sample of 120 Arkansas residents and for a random sample of 180 Virginia residents. Use the homestate.xlsx data file.

(a) Formulate hypotheses that can be used to determine whether the percentage of stay-at- home residents in the two states differs from the overall average of 57.7%.

(b) Estimate the proportion of stay-at-home residents in Arkansas. Does this proportion differ significantly from the mean proportion for all states? Use α = 0.05.

(c) Estimate the proportion of stay-at-home residents in Virginia. Does this proportion differ significantly from the mean proportion for all states? Use α = 0.05.

(d) Would you expect the proportion of stay-at-home residents to be higher in Virginia than in Arkansas? Support your conclusion with the results obtained in parts (b) and (c).

Question 2

Using the late shipments.fst:

(a) Calculate the proportion of late shipments.

(b) Calculate the mean, median and standard deviation of pack price for the shipment modes.

(c) Analyse the distribution of pack price for the different shipment modes using a box plot.

(d) Identify the shipment mode, manufacturing and country locations, and the packing price of the outliers.

(e) Run linear regression of pack price on shipment mode.

(f) Perform ANOVA on the regression model.

(g) Comment on the differences in pack price across the different shipment modes.

(h) Perform a proportion test to check whether being late shipments vary across product groups.

(i) Check the differences in median of weight across product group and shipment mode.