The average number of times Americans dine out in a week fell from 4.0 in 2008 to 3.8 in 2012 (Zagat.com, April 1, 2012). The number of times a sample of 20 families dined out last week provides the following data: 6 1 5 3 7 3 0 3 1 3 1 2 4 1 0 5 6 3 1 4

Complete the following in Excel:

a. Compute the mean and median.

b. Compute the first and third quartiles.

c. Compute the range and interquartile range.

d. Compute the variance and standard deviation.

e. The skewness measure for these data is 0.34. Comment on the shape of this distribution. Is it the shape you would expect? Why or why not?

f. Do the data contain outliers?

A roll of plastic-coated wire has an average of 0.09 flaws per 5-meter length of wire. Suppose a quality control engineer will sample a 5-meter length of wire from a roll of wire 230 meters in length. If no flaws are found in the sample, the engineer will accept the entire roll of wire.

a. What is the probability that the roll will be rejected?

b. Before examining the sample, what is the probability that there are no flaws in the 230 meters of wire? What is the probability that there are exactly 3 flaws in the entire roll?

c. Based on your answers from parts (a) and (b), what is the probability that if there is at least one flaw in the entire roll, a randomly sampled 5-meter length of wire from that roll will have at least one flaw? [Hint: It may be helpful to recognize that if the roll has no flaws, the 5-meter length of wire will have no flaws.]

d. Given that no flaws were found in the sample, what is the probability that the entire roll has no flaws? Is sampling 5 meters of wire sufficient for determining if the entire roll has flaws? Why or why not?

3) The Wall Street Journal reported that recipients of a bachelor degree with major in business receive average starting salaries of $55,000 in 2017, with a standard deviation of $4,000. A sample of 100 salaries from business majors collected in 2018 shows a mean starting salary of $ $54,000. You are hired as a statistician to investigate whether there are salary differences for business majors in 2018 with respect to 2017. Allow for 5% error on a two tail test.

3.A) The critical value for this problem is?

3.B) The calculated a standard error is equal to?

3.C) The test statistic calculated is?

3.D) What is your decision after the test? (Accept or Reject)

3.E) What is the p-value equal to?

3.F) What is your conclusion after the test? Be specific and relate to the problem.

In studying his campaign plans, Mr. Singleton wishes to estimate the difference between men's and women's views regarding his appeal as a candidate. He asks his campaign manager to take two random independent samples and find the 98% confidence interval for the difference. A random sample of 653 male voters and 560 female voters was taken. 226 men and 271 women favored Mr. Singleton as a candidate. Find this confidence interval.

Step 1 of 3:

Find the point estimate that should be used in constructing the confidence interval. Round your answer to three decimal places.

Step 2 of 3:

Find the margin of error. Round your answer to six decimal places.

Step 3 of 3:

Construct the 98% confidence interval. Round your answers to three decimal places.

Companies often have different mutual funds to serve different investment time horizons. Use the tab titled BESTFUNDS to determine if there is a difference between in the three-year annualized return for small cap growth, mid-cap growth, and large cap growth mutual funds. (a) Identify which type of test you plan to use and why. (b) Analyze and report your findings. (c) Put the findings into meaningful words (i.e., explain what the test allows you to conclude about the types of mutual funds). (d) Does your result from (b) give you statistical permission to probe group differences, yes or no?

A sociologist records the annual household income (in thousands of dollars) among a sample of families living in a high-crime neighborhood. Locate the lower, median, and upper quartiles for the times listed below. Hint: First arrange the data in numerical order. lower quartile thousand dollars median thousand dollars upper quartile thousand dollars 33 55 39 44 34 48 25 39 23 45

Assume that a simple random sample has been selected from a normally distributed population and test the given claim. Identify the null and alternative​ hypotheses, test​ statistic, P-value, and state the final conclusion that addresses the original claim. A simple random sample of 25 filtered 100 mm cigarettes is​ obtained, and the tar content of each cigarette is measured. The sample has a mean of 18.8 mg and a standard deviation of 3.64 mg. Use a 0.05 significance level to test the claim that the mean tar content of filtered 100 mm cigarettes is less than 21.1 mg, which is the mean for unfiltered king size cigarettes. What do the results​ suggest, if​ anything, about the effectiveness of the​ filters?

What are the​ hypotheses?

Identify the test statistic.​(Round to three decimal places as​ needed.)

Identify the​ P-value.

The​ P-value is(Round to four decimal places as​ needed.)

State the final conclusion that addresses the original claim.

What do the results​ suggest, if​ anything, about the effectiveness of the​ filters?

The patient recovery time from a particular surgical procedure is normally distributed with a mean of 3 days and a standard deviation of 1.5 days. Let X be the recovery time for a randomly selected patient. Round all answers to 4 decimal places where possible.

a. What is the distribution of X? X ~ N(,)

b. What is the median recovery time? days

c. What is the Z-score for a patient that took 4.8 days to recover?

d. What is the probability of spending more than 4 days in recovery? e. What is the probability of spending between 2.8 and 3.4 days in recovery? f. The 70th percentile for recovery times is days.

Given a normal distribution with μ=55 and σ=4​, complete parts​ (a) through​ (d).

a) What is the probability that X>48​? ​(Round to four decimal places as​ needed.)

b) What is the probability that X<47​? ​(Round to four decimal places as​ needed.)

c) For this distribution, 6% of the values are less than what X-Value? ​(Round to four decimal places as​ needed.)

d) Between what two X-values (symmetrically distributed around the​ mean) are 60% of the values? ​(Round to four decimal places as​ needed.)

Television viewing reached a new high when the global information and measurement company reported a mean daily viewing time of 8.35 hours per household. Use a normal probability distribution with a standard deviation of 2.5 hours to answer the following questions about daily television viewing per household.

a. what is the probability that a household views television between 3 and 10 hours a day (to 4 decimals)

b. how many hours of television must a household have in order to be in the top 4% of all television viewing households (to 2 decimals)

c. what is the probability that a household views television more than 5 hours a day (to 4 decimals)

Mutual funds mix different types of investments which alters performance. Use the tab titled BESTFUNDS1 to determine if there is a difference between the one-year and three-year annualized return for the 20 mutual funds shown in the file. (a) Identify which type of test is most appropriate for you to use, justify your answer. (b) Determine whether or not the mean return differs for the two investment horizons (use α = .05). (c) Make sure to interpret the results for real-world use (i.e., explain what the test allows you to conclude about the mutual funds).

A hotel manager is looking to enhance the initial impression that hotel guests have when they check in. Believed to contribute to initial impressions is the time it takes to deliver a guest’s luggage to his or her room after check-in. A random sample of 20 deliveries on a particular day were selected from Wing A of the hotel, and a random sample of 20 deliveries were selected in Wing B (i.e., the Excel tab LUGGAGE). (a) Identify which type of test is most appropriate for you to use, justify your answer. (b) Determine whether or not the mean delivery time differs for the two wings of the hotel (use α = .05). (c) If faster luggage delivery time is positively related to guests’ initial impression, which wing(s) should receive the highest impression ratings?

If the true data generating process is normal, how will the

bin widths of Scott's rule and Freedman-Diaconis compare?

After living together for a year, Mary, Martha, and Alice have decided to go their separate ways. They have several items they bought together as well as some moving-out chores to divide. The values they place on each are given below. Using the sealed bids method, find the final allocation