01:960:401:H6

THIRD EXAM SUMMER 2022

Instructions:

1. Name: _______________________________ ID Number: ____________________________

2. Check your exam: there are 10 problems on 6 pages. Show your work here or in an extra page.

3. This is expected to be a personal exam. The exam is due on (one minute before noon)

**1****.- **Suppose you want to estimate the difference between two population means correct to within 1.8 with a 95% confidence interval. If prior information suggests that the population variances are approximately equal to σ_{1}^{2} = σ_{2}^{2} = 14 and you want to select independent random samples of equal size from the populations, how large should the sample sizes, n1 and n2, be? (Show your work)

*Answer:*

**2.-** One of the most serious health problems in India is malaria. Consequently, Indian hospital administrators must have the resources to treat the high volume of malaria patients that are admitted. A research institute investigated whether the malaria admission rate is higher in some months than in others. In a sample of 192 hospital patients admitted in January, 32 were treated for malaria. In an independent sample of 403 patients admitted in May (4 months later), 34 were treated for malaria.

a). Give a point estimate of the difference in the malaria admission rates in January and May.

*Answer:*

b). Find a 90% confidence interval for the difference in the malaria admission rates in January and May.

*Answer:*

**3.-** Independent random samples selected from two normal populations produced the sample means and standard deviations shown below.

a) Conduct the test of H_{0}: µ_{1} – µ_{2} = 0 versus

H_{a}: µ_{1} – µ_{2} ≠ 0 with α = 0.05

b) Built a 95% CI for µ_{1} – µ_{2}

*Answers:*

**4**.- Currently, quarters have weights that are normally distributed with a mean of 5.670 g and a standard deviation of 0.062 g. A vending machine is configured to accept only those quarters with weights between 5.550 g and 5.790 g.

a). If 280 different quarters are inserted into the vending machine, what is the expected number of rejected quarters?

b). If 280 different quarters are inserted into the vending machine, what is the probability that the mean falls between the limits of 5.550 g and 5.790 g?

c. If you own the vending machine, which result would concern you more? The result from part (a) or the result from part (b)? Why?

5**.- **.- In a survey about attitudes toward marriage, 24% of 205 single women said that they “definitely want to get married.” In the same survey, 27% of 260 single men gave that same response. Use a 0.01 significance level to test the claim that there is a gender gap on the attitude toward marriage.

*Answer: **Fill in the equality expressions below*

H_{0}: H_{a}: α = n_{1} = n_{2} = _{1} = _{2} =

Critical Values = Rejection Region = Test statistic =

Conclusion: Reject H_{0} Keep H_{0}

P-value = 98% CI =

**6.-** Determine whether r is positive, negative, or zero for each of the following data sets.

**7.-** You have interest in finding the correlation, if any, between height of an eruption and time intervals after eruptions of the Old Faithful geyser. Using the data given below, is there a linear correlation between height of an eruption and the time interval after the eruption?

Height 140 110 125 120 140 120 125 150

Interval after 92 65 72 94 83 94 101 87

a) Using the data given above, generate a scatter plot.

b) if the software gives for r the following value 0.2683, is this a significant value?

c) If the regression analysis shows the following results

can you get a conclusion about the correlation coefficient r based on the slope coefficient? Is there a relationship between r and b_{1}, the regression slope?

**8.- **Randomly selected subjects were asked about use of marijuana for medical purposes. Use a 0.05 significance level to test the claim that response to the question is independent of gender.

In favor Oppose Don’t’ know

Men 538 167 29

Women 557 186 31

What is your conclusion?

Find DF, the Chi-square test, and the p-value.

9.- Five strains of cultured Staphylococcus aureus—bacteria that cause staph infections—

were observed for 24 hours at 27◦C. The following table reports bacteria counts, in millions, for different cases from each of the five strains.

Strain A Strain B Strain C Strain D Strain E

9 3 10 14 33

27 2 47 18 43

22 7 50 17 28

30 5 52 29 59

16 2 26 20 31

a) Test the null hypothesis H_{0}: µ_{1} = µ_{2} = µ_{3} = µ_{4} = µ_{5} using the ANOVA table below

Answer:

b) You run the Tukey method for pairwise comparisons.

What are your conclusions? Which strains are similar and which are different in terms of bacterial growth.

10.- The table below lists body temperatures obtained from randomly selected subjects. The temperatures are categorized according to gender and whether the subject smokes. Using a

0.05 significance level, test for an interaction between gender and smoking, test for an effect from gender, and test for an effect from smoking. What do you conclude?

Smokes Does Not Smoke

Male 96.0 97.0 95.0 96.0 98.0 98.0 98.8 97.0

Female 98.0 96.0 96.0 97.0 97.7 98.0 98.2 99.1

Answer: (which hypothesis you reject or you keep?)

a) The test for interaction means _________________

b) The test for Smoking means ____________________

c) The test for Gender means ____________________

d) the Tukey test means ________________________

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