A random sample is drawn from a normally distributed population with mean μ = 23 and standard deviation σ = 2.6. [You may find it useful to reference the z table.]

a. Are the sampling distribution of the sample mean with n = 31 and n = 62 normally distributed?

• Yes, both the sample means will have a normal distribution.

• No, both the sample means will not have a normal distribution.

• No, only the sample mean with n = 31 will have a normal distribution.

• No, only the sample mean with n = 62 will have a normal distribution.

b. Calculate the probabilities that the sample mean is less than 23.7 for both sample sizes. (Round intermediate calculations to at least 4 decimal places, “z” value to 2 decimal places, and final answer to 4 decimal places.)

According to the National Automobile Dealers Assoc., 75% of U.S. car dealers' profits comes from repairs and parts sold. However, many of the dealerships' service departments aren't open evenings or weekends. The percentage of dealerships opened during the evenings and weekends are as follows:

a. Are the listed times mutually exclusive?

b. What is the probability that a car dealership selected at random is not open in the evenings or on the weekends?

c. Suppose two car dealerships, say, Dealership A and Dealership B, are each selected at random from car dealerships in the United States. What is the probability that both are open in the evenings but not on the weekends, or that both are open on the weekends but not in the evenings?

d. For the two dealerships in part c, what is the probability that Dealership A is open in the evenings but not on the weekends, and Dealership B is open on the weekends but not in the evenings?

e. For the two dealerships in part c, what is the probability that one of them is open in the evenings but not on the weekends, and that the other is open on the weekends but not in the evenings?

. A highway department executive claims that the number of fatal accidents which occur in her state does not vary from month to month. The results of a study of 170 fatal accidents were recorded. Is there enough evidence to reject the highway department executive's claim about the distribution of fatal accidents between each month?

Month Jan Feb Mar Apr May Jun Jul Aug Sep Oct Nov Dec Fatal Accidents :

11 19 24 16 11 7 7 17 9 19 18 12

State the null and alternative hypothesis.

What does the null hypothesis indicate about the proportions of fatal accidents during each month?

State the null and alternative hypothesis in terms of the expected proportions for each category.

Find the value of the test statistic. Round your answer to three decimal places.

Find the degrees of freedom associated with the test statistic for this problem.

Find the critical value of the test at the 0.01 level of significance. Round your answer to three decimal places.

Make the decision to reject or fail to reject the null hypothesis at the 0.01 level of significance.

State the conclusion of the hypothesis test at the 0.01 level of significance.

Post a description of the types of probability and nonprobability sampling you selected. Then describe two strengths and two weaknesses of each type of sampling. Finally, identify two ethical considerations that may factor into selecting a sampling method and explain how you might address these considerations.

Using the data below, suppose we focus on the proportions of patients who show improvement. Is there a statistically significant difference in the proportions of patients who show improvement between treatments 1 and 2. Run the test at a 5% level of significance.

Resistance training is a popular form of conditioning aimed at enhancing sports performance and is widely used among high school, college, and professional athletes, although its use for younger athletes is controversial. Researchers obtained a random sample of 3933 patients between the ages of 8 and 30 who were admitted to U. S. emergency rooms with injuries classified by the Consumer Product Safety Commission code "weight-lifting." These injuries were further classified as " accidental" if caused by dropped weight or improper equipment use. Of the 3933 weight-lifting injuries, 1648 were classified as accidental.

What is a 98% confidence interval for the proportion of weight-lifting injuries in this age group that were accidental?

The 98% confidence interval (±±0.001) is from  to

Erin O'Brien, Director of Consumer Credit with Auckland First Bank (AFB), has implemented a 'fast feedback' to keep her informed of the default rate on personal loans at AFB member banks. On each Friday, the default rate is calculated for a sample of 500 personal loans. Last Friday's sample contained 30 defaulted loans. The 90% confidence interval for the population proportion is _________. Select one: a. 0.046 to 0.074 b. 0.039 to 0.081 c. 0.043 to 0.077 d. 0.028 to 0.060

Sixty eight cities provided information on vacancy rates (in percent) in local apartments in the following frequency distribution. The sample mean and the sample standard deviation are 9% and 3.2%, respectively. (You may find it useful to reference the appropriate table: chi-square table or F table)

Calculate the value of the test statistic. (Round intermediate calculations to at least 4 decimal places and final answer to 3 decimal places.)

Make Excel do all calculations, using cell addresses. Don’t type numbers in your formulas.

Report the answers to the questions in your worksheet using the appropriate symbols (µ σ) and notation p(x>=5), p(X<3) etc...

            Use Insert/Symbol to find mu and sigma for mean and std dev.

1. An auditor for Health Maintenance Services of Georgia reports 30 percent of policyholders 55 years or older submit a claim during the year. Twelve policyholders are randomly selected for company records.

a. What type of distribution is this likely to be?

b. What is the expected number (mean) of the distribution?

c. What is the standard deviation of the distribution?

Use the tables in your text to answer the following questions

d. What is the probability that exactly 6 of the 12 policyholders have filed a claim?

e. What is the probability that more than 6 of the 12 policyholders have filed a claim?

f. What is the probability that 6 or fewer of the 12 policyholders have filed a claim?

g. What is the probability that at least 6 of the 12 policyholders have filed a claim?

Use the BINOMDIST function to answer the following questions

h. What is the probability that exactly 8 of the 12 policyholders have filed a claim?

i. What is the probability that more than 8 of the 12 policyholders have filed a claim?

j. What is the probability that 8 or fewer of the 12 policyholders have filed a claim?

k. What is the probability that at least 8 of the 12 policyholders have filed a claim?

A electronics manufacturer has developed a new type of remote control button that is designed to operate longer before failing to work consistently. A random sample of 20 of the new buttons is selected and each is tested in continuous operation until it fails to work consistently. The resulting lifetimes are found to have a sample mean of ?¯ = 1260.4 hours and a sample standard deviation of s = 116.1. Independent tests reveal that the mean lifetime of the best remote control button on the market is 1200 hours. Conduct a hypothesis test to determine if the new button's mean lifetime exceeds 1200 hours. Round all calculated answers to four decimal places.

1. The null hypothesis is ?0:?=1200. What is the alternate hypothesis? A. ??:?=1260.4 B. ??:?>1200 C. ??:?≠1200 D. ??:?<1200 E. ??:?>1260.4

2. Which of the following conditions must be met to perform this hypothesis test? Select all the correct answers. A. The number of remote control buttons tested must be normally distributed. B. We must be able to expect that at least 5 buttons will fail to work consistently. C. The sample must be large enough so that at least 10 buttons fail and 10 succeed. D. The observations must be independent. E. The lifetime of remote control buttons must be normally distributed.

3. Calculate the test statistic =

4. Calculate the p-value

5. Calculate the effect size, Cohen's d, for this test. ?̂ =

6. The results of this test indicate we have a... A. moderate to large B. large C. small D. small to moderate effect size, and... A. some evidence B. little evidence C. very strong evidence D. extremely strong evidence E. strong evidence that the null m odel is not compatible with our observed result.

Research the role of ETL tools in providing clean and purposely transformed data as part of data mining processes. Then explain the role of ETL in data mining and statistical analysis.

Use Minitab to answer the questions. Make sure to copy all output from the Minitab:

1.   Followings Tables shows previous 11 months stock market returns.

1. Let’s consider the population mean of SP500 as µ1 and that of DJIA as µ2 while none of population variance is known. Test following hypothesis:

Ho : µ1 = µ2

Ha :   µ1 ≠ µ2

2. Let’s consider the population variance of SP500 as σ²₁ and that of DJIA as σ²₂, and none of them are known. Test following hypothesis:

Ho :   σ²₁ = σ²₂

Ha :   σ²₁ ≠ σ²₂

6) Perform the following hypothesis test

Ho :   σ²₁ ≤ σ²₂

Ha :   σ²₁ > σ²₂

A recent study claimed that at least 15% of junior high students are overweight. In a sample of 160 students, 18 were found to be overweight. Test the claim, using α = 0.05.

1. State the null and alternative hypotheses for the test. [3 marks]

(b) Calculate the value of the test statistic for this test. [2 marks]

(c) Calculate the p-value for this test. [2 marks]

(d) State the conclusion of this test. Give a reason for your answer