Statistics homework help. Interpret the results in Part I and part II.

__Part I ( 25 points)__

Find the standard-normal curve area that lies:

- To the right of 0.65
- To the left of z = -2.13
- 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)__

- 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?

- 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?

- Identify the claim. State the null and alternative hypotheses
- Identify the level of significance, the critical value and the direction of the test
- Find the standardized test statistic z.
- Construct the rejected region and decide whether to reject the Null Hypothesis.
- Find the p-value
- Interpret the result in the context of the original claim

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** 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 |

- Use a calculator to find Σx, Σy, Σx
^{2}, Σy^{2}and Σxy. - 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.
- Would you say the correlation is low, moderate, or strong? State whether it is positive or negative?
- Make a Prediction for 10 employees