A grocery store is analyzing their sales. A sample of 40 receipts has an average value of $137 and standard deviation of $30.20 Use this information to test whether or not the mean in sales value at this store is different from $150? Use?= 0.1

a. State null & alternate hypotheses

b. Calculate Z test statistic

c. Determine Z critical

d. State conclusion CLEARLY with the evidence.

12. A hospital group operates 33 clinics in Indiana and Illinois. A study was conducted to estimate the difference in mean time spent per visit for men and women. Previous studies indicated that the standard deviation is 11 min, for men and 16 min. for women. A random sample of 100 men and 100 women at the two states was observed. The resulting sample means were 34.5 min. for men and 42.4 min. for women. Is the difference between men and women significant at?= 0.05

a. State null & alternate hypotheses

b. What is the ‘degree of freedom’?

c. Calculate t test statistic

d. Determine t critical

e. Is the difference in mean time between men and women significant?

13. Answer this question using the internet or other sources. You must quote the references you cited. Explain clearly the following terms in a paragraph.

(a) Random

(b) Independent

(c) Degree of Freedom

14. Solar cells are attached to a panel with a new heat resistant adhesive. The adhesive must provide 2.80 pounds of force in order to hold the cell on the panel. A random sample of 50 cells is tested and the following forces are necessary to break the adhesive.

2.65 2.76 2.82 2.89 2.95

2.67 2.77 2.83 2.90 2.95

2.68 2.77 2.84 2.90 2.97

2.68 2.77 2.84 2.91 2.98

2.70 2.78 2.84 2.92 2.98

2.70 2.78 2.85 2.92 2.99

2.73 2.79 2.88 2.93 3.00

2.74 2.80 2.88 2.93 3.01

2.75 2.81 2.88 2.93 3.02

2.75 2.82 2.89 2.94 3.03

(a) Test at the 0.01 level of significance the hypothesis that the mean adhesive strength is at least 2.80 pounds.

(b) Assuming the data follow a normal distribution, what proportion of the cells would you estimate to be out of tolerance(i.e., less than 2.80 pounds of adhesive strength)?

(c) Discuss your results from part a and b above. Is a test for the mean appropriate in this case? Why or why not?

15. A medical researcher is testing a new drug to see if it slows the growth of malignant tumors in rats. The control group of 40 rats is given none of the drug and the test group of 40 rats is given a dose every day for two weeks. At the end of the test, the following statistics were calculated.

**Control Rats**** Test Rats**

**Average growth of tumor** 6.2 grams 4.1 grams

**Standard Deviation **3.1 grams 2.8 grams

Conduct the appropriate hypothesis test to determine if the new drug appears to slow the mean rate of tumor growth.

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