DU Business Statistics Inference for Counts Questions

1.Are food delivery apps equally popular? A 2019 study asked

160

U.S. adults who regularly use a food delivery app which one they used most recently. The results are shown in the table below.

160

Research Question: Does this study provide evidence that the food delivery apps are not equally likely among U.S. adults who regularly use a food delivery app?

Ho:Ha:

b.How many of the 160 players do we expect to see make each of the choices if the choices are equally distributed among the four options? (1 pt)

c.Bonus Question:Find the chi-square test statistic for investigating this research question by hand. Show your work to receive full credit. If you’d like, you can show your work on paper, take a picture, and insert the picture here. (2 pts)

d.Carry out the goodness-of-fit test in StatCrunch and find the p-value for investigating this research question (include a screenshot of your StatCrunch output showing the correct p-value to receive credit). (2 pts)p-value: Paste a screenshot here

e.Write a conclusion in the context of the research question. (2 pts)

2.Cocaine addiction is very hard to break. Even among addicts trying hard to break the addiction, relapse is common. A relapse is when a person trying to break out of the addiction fails and uses cocaine again. A study was conductd to investigate the effectiveness of two drugs, desipramine and lithium, in the treatment of cocaine addiction. The subjects in the six-week study were cocaine addicts seeking treatment. The 72 subjects were randomly assigned to one of three groups: desipramine, lithium, or a placebo, with 24 subjects in each group. Ten of the subjects taking desipramine relapsed, 18 of the subjects taking lithium relapsed, and 20 of those taking the placebo relapsed.

The researcher is interested in whether the proportion of subjects who relapse differs depending the treatment group.

• Complete the two-way table of the data below, including the row and column totals. (2 pts)

Total

Total

b.Find the relevant conditional proportions (i.e., find the proportion that relapsed in each group). (1 pt)Relapse | Desipramine =

Relapse | Lithium =

Relapse | Placebo =

c.Recall the research question as stated up above. Convert this research question into a null and alternative hypothesis. You can write the hypotheses using either words or symbols. (2 pts)Ho:Ha:

d.Use StatCrunch to carry out the chi square test for independence to obtain an exact p-value for this investigation. Clearly state the p-value, and copy and paste the StatCrunch output from the test below. (3 pts)p-value:Copy and paste screenshot here

e.Use the p-value from part d to evaluate the evidence and draw a conclusion based on this test, and write this conclusion in the context of the problem. (2 pts)

f.Find a 95% confidence interval for difference in the proportion who relapse in the Lithium group compared to the Placebo group. (2 pts)

Upper limit:

Lower limit:

g.Based on the confidence interval found above, can we conclude a statistically significant difference exists in the proportion that relapse between the lithium group and the control group? Explain your reasoning. (1 pt)