Statistics assignment

Interpret the results in Part I and part II.

Part I ( 25 points)

Find the standard-normal curve area that lies:

a) To the right of 0.65

b) To the left of z = -2.13

c) Between z = -0.34 and z = 0.62.

d) A tire store finds that the thread life of its tires is normally distributed, with a mean of 26,640 miles and a standard deviation of 4000 miles. The store sold 9000 tires this month. How many of them can be expected to last between 25,000 and 30,000 miles?

Part II ( 15 points)

a) From a random sample of 36 business days, the average closing price of Apple Stock was $116.16 with a standard deviation of $10.27. Construct a 90% and 95% confidence interval. Which interval is wider?

b) Determine the minimum sample size required when you want to be 95% confident that the sample mean is within one unit of the population mean and σ=4.8. (population standard deviation)

Part III (Hypothesis testing ( 30 points)

A company that makes cola drinks states that the mean caffeine content per 12-ounce bottle of cola is 40 milligrams. You want to test this claim. During your tests, you find that a random sample of twenty 12 ounce-bottles of cola has a mean caffeine content of 39.2 milligrams. Assume the population is normally distributed and the population standard deviation is 7.5 milligram. At α = .01, can you reject the company’s claim?

a) Identify the claim. State the null and alternative hypotheses

b) Identify the level of significance, the critical value and the direction of the test

c) Find the standardized test statistic z.

d) Construct the rejected region and decide whether to reject the Null Hypothesis.

e) Find the p-value

f) Interpret the result in the context of the original claim

Part IV ( 30 points) The table below showed the average number of employees(x) in a group health insurance plan and the average administrative cost(y) as a percentage of claims.

x	3	6	12	18	24
y	60	95	140	170	185

a) Use a calculator to find Σx, Σy, Σx2, Σy2 and Σxy.

b) Compute r, the slope , the intercept, the regression line and indicate as x increase does the value of r imply that y should tend to increase or decrease? Explain.

c) Would you say the correlation is low, moderate, or strong? State whether it is positive or negative?

d) Make a Prediction for 10 employees