Data from the Office for National Statistics show that the mean age at which men in Great Britain get married was 32.5. A news reporter noted that this represents a continuation of the trend of waiting until a later age to wed. A new sample of 47 recently wed British men provided their age at the time of marriage. These data are contained in the Excel Online file below. Construct a spreadsheet to answer the following questions.

Open spreadsheet

Do these data indicate that the mean age of British men at the time of marriage exceeds the mean age in 2013? Test this hypothesis at . What is your conclusion? Use the obtained rounded values in your calculations.

Because -value _________≤> , we _________rejectfail to reject . There is _________insufficientsufficient evidence to conclude that the mean age at which British men get married exceeds what it was in 2013.

• How is data analytics different from statistics?
• Analytics tools fall into 3 categories:descriptive, predictive, and prescriptive. What are the main differences among these categories?
• Explain how businesses use analytics to convert raw operational data into actionable information. Provide at least 1 example

The lengths of pregnancies in a small rural village are normally distributed with a mean of 270 days and a standard deviation of 13 days.

In what range would you expect to find the middle 50% of most pregnancies?
Between and .

If you were to draw samples of size 51 from this population, in what range would you expect to find the middle 50% of most averages for the lengths of pregnancies in the sample?
Between and .

How do you add an error bar when the add error bar is not included in the add chart element box? How do you do the dependent t-test calculation in excel?

With a new mass shooting nearly every day, it is not surprising that violent crime is on everyone’s minds.   Using the FBI’s crime statistics from randomly selected U.S. cities, answer the following questions:

Perform a correlation. What is the correlation coefficient?

If there IS a correlation, what other variables may be acting as intervening variables (e.g., causing the change in crime rate making it appear as if there is a relationship when one doesn’t exist.)?

If there is NOT a relationship, between unemployment and violent crime, can you think of any variables that might be acting as suppressors (i.e. dampening a relationship that might actually be there)?

Perform a regression to predict violent crime. Show your regression analysis.

Write out the prediction model.

What does the model tell you?

Are the model’s results accurate and reliable? How do you know?

what jumps out as a MAJOR issue with the crime data?

An instructor has given a short quiz consisting of two parts. For a randomly selected student, let X = the number of points earned on the first part and Y = the number of points earned on the second part. Suppose that the joint pmf of X and Y is given in the accompanying table.

(a) Compute the covariance for X and Y. (Round your answer to two decimal places.)
Cov(X, Y) =

(b) Compute ρ for X and Y. (Round your answer to two decimal places.)
ρ =

In a bimodal histogram, the two highest bars will have the same height.

True or False

A national health organization warns that 30% of middle school students nation wide have been drunk. A local health agency randomly surveys 100 students and only 25 report having been drunk. Construct an appropriate 80% confidence interval.

A. 0.25

B. 0.0555

C. 0.1946 to 0.3055

D. 0.1651 to 0.3349

Please show work and exaplain why. Thank you!

The federal government recently granted funds for a special program designed to reduce crime in high-crime areas. A study of the results of the program in high-crime areas of Miami, Florida, are being examined to test the effectiveness of the program. The difference in crimes reported is calculated as (crimes after - crimes before). You want to test whether the average number of crimes reported after are different from the average number of crimes reported before. What are the hypotheses for this test?

Question 10 options:

Question 11 (1 point)

Will eating oatmeal promote healthy levels of cholesterol? A consumer reports analyst took a sample of 39 people with high cholesterol and asked them to eat oatmeal once a day for 3 months. Measurements were taken of their cholesterol levels before and after the 3 months in mg/dl. The analyst is testing whether the cholesterol levels after the diet are different from the cholesterol levels before the diet. The hypotheses for this test are as follows: Null Hypothesis: μ_D = 0, Alternative Hypothesis: μ_D ≠ 0. If the analyst calculated the mean difference in cholesterol levels (after - before) to be 0.69 mg/dL with a standard deviation of 5.06 md/dL, what is the test statistic and p-value for the paired hypothesis t-test?

Question 11 options:

Question 12 (1 point)

A new gasoline additive is supposed to make gas burn more cleanly and increase gas mileage in the process. Consumer Protection Anonymous conducted a mileage test to confirm this. They took a sample of their cars, filled it with regular gas, and drove it on I-94 until it was empty. They repeated the process using the same cars, but using the gas additive. Using the data they found, they performed a paired t-test with data calculated as (with additive - without additive) with the following hypotheses: Null Hypothesis: μ_D ≤ 0, Alternative Hypothesis: μ_D > 0. If they calculate a p-value of 0.8488 in the paired samples t-test, what is the appropriate conclusion?

Question 12 options:

Question 13 (1 point)

Suppose the national average dollar amount for an automobile insurance claim is $795.62. You work for an agency in Michigan and you are interested in whether or not the state average is greater than the national average. The hypotheses for this scenario are as follows: Null Hypothesis: μ ≤ 795.62, Alternative Hypothesis: μ > 795.62. Suppose the true state average is $920.27 and the null hypothesis is not rejected, did a type I, type II, or no error occur?

Question 13 options:

Question 14 (1 point)

Consumers Energy states that the average electric bill across the state is $48.63. You want to test the claim that the average bill amount is actually different from $48.63. The hypotheses for this situation are as follows: Null Hypothesis: μ = 48.63, Alternative Hypothesis: μ ≠ 48.63. If the true statewide average bill is $48.63 and the null hypothesis is rejected, did a type I, type II, or no error occur?

Question 14 options:

It is reported in USA Today that the average flight cost nationwide is $442.28. You have never paid close to that amount and you want to perform a hypothesis test that the true average is actually greater than $442.28. What are the appropriate hypotheses for this test?

Question 1 options:

Question 2 (1 point)

In the year 2000, the average vehicle had a fuel economy of 23.13 MPG. You are curious as to whether the average in the present day is greater than the historical value. The hypotheses for this scenario are as follows: Null Hypothesis: μ ≤ 23.13, Alternative Hypothesis: μ > 23.13. A random sample of 43 vehicles shows an average economy of 24.15 MPG with a standard deviation of 6.69 MPG. What is the test statistic and p-value for this test?

Question 2 options:

Question 3 (1 point)

Consumers Energy states that the average electric bill across the state is $41.553. You want to test the claim that the average bill amount is actually greater than $41.553. The hypotheses for this situation are as follows: Null Hypothesis: μ ≤ 41.553, Alternative Hypothesis: μ > 41.553. A random sample of 47 customer's bills shows an average cost of $43.307 with a standard deviation of $8.0202. What is the test statistic and p-value for this test?

Question 3 options:

Question 4 (1 point)

A medical researcher wants to determine if the average hospital stay of patients that undergo a certain procedure is different from 8.7 days. The hypotheses for this scenario are as follows: Null Hypothesis: μ = 8.7, Alternative Hypothesis: μ ≠ 8.7. If the researcher takes a random sample of patients and calculates a p-value of 0.0197 based on the data, what is the appropriate conclusion? Conclude at the 5% level of significance.

Question 4 options:

To gain access to his account, a customer using an automatic teller machine (ATM) must enter a 6-digit code ( 0 to 9). If repetition of the same digit is not allowed (for example, 555561 or 333333), how many possible combinations are there?(The first digit can not be zero)

a)151200 b)136080 c)1,000,000 d)900,000

1.Test the hypothesis that the proportion of students who have the Wuhan flu is .3. Use a .10 significance level, a two-tail test and the following data: A sample of 100 students has 40 with the virus.

2 Test the hypothesis that the mean number of hours the Wuhan flu can live on a cell phone is more than 20. Use a .01 significance level and a one tail test and the following data: a sample of 50 phones has a sample mean =21.5 and a variance=9.

3 Test the null hypothesis that the proportion of students who believe TRUMP policy is appropriate dealing with the TRUMP virus is .6. The alternative hypothesis is the proportion >.6. Use a .05 significance level. A sample of 25 students has 19 think TRUMP policy is effective.

4) Are students avoiding events that average more than 20 people? A sample of 25 event has an average attendance of 23.3 people and a variance of 4 people. Use a significance level of 5% and a one-tail test.

5. Is the vaccine effective for the Wuhan flu? A sample of 30 students were given the vaccine and 12 got the virus. Without the vaccine, the rate of infection is 50%. Use a 1 tail test and a 5% significance level. What is the p value. [Khan academy has a good discussion of the P value]

6. Do students spend more than 6 ours a day on the phones? A sample of 150 students has an average usage of 8 hours and a variance of 6 hours. Use a 10% significance level.

You want to determine the speed limit for a local highway.   

Distribution data for the driving speed on a given street is given below; all speeds have been rounded to the nearest integer.  

Part a: What is the average(mean) and standard deviation of this sample of data? (Hint, you will need to manipulate the data – you cannot use the average or stdev functions in excel on the data as is.)

Part b: What is the value that 85% of the drivers fall under (the 85% speed limit) that you would recommend using this data? Answer the following questions to help you think through this problem.  

• When do you use the respective distribution or inverse functions in excel? Which situation do you have here and how do you know?

• Using that information, what would you recommended speed limit this road? (Think about speed limits and how they are posted?)

Part c: What percent of people drive within 5 mph of your recommended 85% speed limit, using this data?

You will need to use R to compute the final probabilities, but show all of the work up to that point and write down the R code that you ran to compute your final answer. Problems should be done in the order listed, and should be clear and complete for full marks.

1. The tensile strength of plastic used to make grocery bags is an important quality characteristic. It is known that the strength is normally distributed with mean, μ = 2900 psi and standard deviation, σ = 26 psi. If you purchase 50 of these bags, what is the probability that their mean tensile strength is less than 2890 psi?

2. Starting incomes of IT graduates are roughly normally distributed with μ = $50,000 and σ = $6000. If 12 IT graduates are randomly selected, determine the probability that their mean annual income will exceed $55,000.

The following data are costs (in cents) per ounce for nine different brands of sliced Swiss cheese. 27 64 38 44 70 81 47 52 49

a) Calculate the variance for this data set. (Round your answer to three decimal places.)

b) Calculate the standard deviation for this data set. (Round your answer to three decimal places.)