Anystate Auto Insurance Company took a random sample of 370 insurance claims paid out during a 1-year period. The average claim paid was $1580. Assume σ = $250.

Find a 0.90 confidence interval for the mean claim payment. (Round your answers to two decimal places.)

Find a 0.99 confidence interval for the mean claim payment. (Round your answers to two decimal places.)

Let xi, i = 1,2,...,n be independent realizations from a population distributed like a Pareto with unknown mean.

(a) Compute the Standard Error of the sample mean. [Note: By“compute”, I mean “find the formula for”]. What is the probability that the sample mean is two standard deviations larger than the popula-
tion mean?

(b) Suppose the sample mean is 1 and the Standard Error is 2. Con- sider a test of the hypothesis that the population mean is 0, against the alternative that it is greater. What is the p−value? Compute a 5% confidence interval [Note: Use the Normal as an approx- imation for simplicity]. What is the type II error if the actual population mean is 2?

Customers arrive at a grocery store at an average of 2.1 per minute. Assume that the number of arrivals in a minute follows the Poisson distribution. Provide answers to the following to 3 decimal places.

Part a)

What is the probability that exactly two customers arrive in a minute?



Part b)

Find the probability that more than three customers arrive in a two-minute period.



Part c)

What is the probability that at least seven customers arrive in three minutes, given that exactly two arrive in the first minute?

question c is not 0.442

A fitness course claims that it can improve an individual's physical ability. To test the effect of a physical fitness course on one's physical ability, the number of sit-ups that a person could do in one minute, both before and after the course, was recorded. Ten individuals are randomly selected to participate in the course. The results are displayed in the following table. Can it be concluded, from the data, that participation in the physical fitness course resulted in significant improvement?  

Let d=(number of sit-ups that can be done after taking the course)−(number of sit-ups that can be done prior to taking the course). Use a significance level of α=0.1 for the test. Assume that the numbers of sit-ups are normally distributed for the population both before and after taking the fitness course.

Sit-ups before 28 48 25 41 23 25 45 21 37 29

Sit-ups after 40 54 43 55 34 42 52 30 49 43

Step 1 of 5 : State the null and alternative hypotheses for the test.

Step 2 of 5: Find the value of the standard deviation of the paired differences. Round your answer to one decimal place.

Step 3 of 5: Compute the value of the test statistic. Round your answer to three decimal places.

Step 4 of 5: Find the p-value for the hypothesis test. Round your answer to four decimal places.

Step 5 of 5: Draw a conclusion for the hypothesis test.

Assume that​ women's heights are normally distributed with a mean given by mu equals 62.2 in​, and a standard deviation given by sigma equals 1.9 in.

Complete parts a and b.

a. If 1 woman is randomly​ selected, find the probability that her height is between 61.9 in and 62.9 in. The probability is approximately nothing. ​(Round to four decimal places as​ needed.)

b. If 14 women are randomly​ selected, find the probability that they have a mean height between 61.9 in and 62.9 in. The probability is approximately nothing. ​(Round to four decimal places as​ needed.)

List some evaluation projects for which nonprobability sampling might be appropriate.

General guidelines:

Use EXCEL or PHStat to do the necessary computer work.

Do all the necessary analysis and hypothesis test constructions, and explain completely.

Read the textbook Chapter 11. Solve the textbook example on page 403, "Mobile Electronics," in order to compare four different in-store locations with respect to their average sales.

Use One-Way ANOVA to analyze the data set, data, given for this homework.

Use 5% level of significance.

1) Do the Levene test in order to compare the variance of the sales level at four different in-store locations.

2) If there are no significant differences between the variance of sales, then conduct the one-way ANOVA hypothesis test to compare the average sales level at four different in-store locations.

3) If you have seen evidence of difference among the average sales levels at these four different in-store locations, then identify which in-store locations have significantly different average sales than other in-store locations, by using the Tukey procedure

Data Set:

The annual per capita consumption of bottled water was 30.7 gallons. Assume that the per capita consumption of bottled water is approximately normally distributed with a mean of 30.7 and a standard deviation of 13 gallons.

a. What is the probability that someone consumed more than 31 gallons of bottled​ water?

b. What is the probability that someone consumed between 25 and 35 gallons of bottled​ water?

c. What is the probability that someone consumed less than 25 gallons of bottled​ water?

d. 99.5% of people consumed less than how many gallons of bottled​ water?

Check My Work

3. There are two machines available for cutting corks for use in wine bottles. The first produces corks with diameters that are normally distributed with an average of 3 cm and a standard deviation of 0.1 cm. The second machine produces corks with diameters that have a normal distribution with an average of 3.04 cm and a standard deviation of 0.02 cm. Acceptable corks have diameters between 2.9 and 3.1 cm.
a.Which machine is most likely to produce an acceptable cork? Justify your answer
b. Of the 1200 corks cut by the second machine in a working day, approximately, how many are not acceptable?

Bags of potato chips have a mean weight of 6 ounces with a standard deviation of 0.2 ounces. There are 100 bags of potato chips in a box.

(i) What is the probability that the total weight of the 100 bags is greater than 603 ounces?

(ii) A potato chip factory produces 1000 boxes of potato chips. What is the probability that more than 70 of these boxes contain more than 603 ounces of potato chips?

Answer the questions below using the appropriate statistical technique. For questions involving the use of hypothesis testing, you must:

1. State the null and research hypotheses

2. Provide the Z(critical), T(critical), or χ 2 (critical) score corresponding to the α threshold for your test

3. Provide your test statistic

4. Provide your decision about statistical significance

A random sample of 350 persons yields a sample mean of 105 and a sample standard deviation of 10. Construct three different confidence intervals to estimate the population mean, using 95%, 99%, and 99.9% levels of confidence. What happens to the interval width as the confidence level increases? Why?

1. A researcher is interested in studying the effect that the amount of fat in the diet and amount of exercise has on the mental acuity of middle-aged women. The researcher used three different treatment levels for the diet and two levels for the exercise. The results of the acuity test for the subjects in the different treatment levels are shown below.

Perform a Two-way analysis of variance (ANOVA) and report the results using correct APA style; report whether significance was found for Factor A, Factor B, and/or an interaction between Factors A and B was found.

If the test statistic is significant, run a post hoc test to determine between what groups significance was found.

Report an effect size for all significant results.

A Gallup poll conducted in November of 2011 asked the following question, “What would you say is the most urgent health problem facing this country at the present time?” The choices were access, cost, obesity, cancer, government interference, or the flu. The responses were access (27%), cost (20%), obesity (14%), cancer (13%), government interference (3%), or the flu (less than 0.5%). The following is an excerpt from the Survey Methods section. “Results for this Gallup poll are based on telephone interviews conducted Nov. 3-6, 2011, with a random sample of 1,012 adults ages 18 and older, living in all 50 U.S. states and the District of Columbia. For results based on a total sample of national adults, one can say with 99.7% confidence that the maximum margin of sampling error is ±4 percentage points.” Prompt Based on this poll, find a 95% confidence interval to estimate the percentage of U.S. adults who feel that access to healthcare is the most urgent health problem facing this country. Interpret your interval in context.