A recent study found that 85​% of​ breast-cancer cases are detectable by mammogram. Suppose a random sample of 13 women with breast cancer are given mammograms. Find the probability that all of the cases are​ detectable, assuming that detection in the cases is independent. The probability that all of the cases of breast cancer are detectable is about

Networking ~ A 2016 study conducted by LinkedIn found that 85% of all jobs are filled via networking - the process of interacting with others to develop professional contacts. Marie is skeptical of this study, and believes that the actual percentage of jobs filled by networking is actually less than 85%. Marie randomly samples recently filled jobs and finds that 80% of them were filled by networking. She conducts a hypothesis test.

The p-value for the test is calculated to be 0.143.

Which of the statements below are correct interpretations of the p-value? You should choose all that are correct interpretations.

Question 7 options:

High-rent district: The mean monthly rent for a one-bedroom apartment without a doorman in Manhattan is $2634.
Assume the standard deviation is $501. A real estate firm samples $106 apartments. Use the TI-84 Plus calculator.

Part 1 of 5
(a) What is the probability that the sample mean rent is greater than $2704? Round the answer to at least four decimal places.
The probability that the sample mean rent is greater than $2704 is?

Part 2 of 5
(b) What is the probability that the sample mean rent is between $2503 and $2603? Round the answer to at least four decimal places.
The probability that the sample mean rent is between $2503 and $2603 is?

Part 3 of 5
(c) Find the 85th percentile of the sample mean. Round the answer to at least two decimal places.
The 85th percentile of the sample mean rent is?

Part 4 of 5
(d) Would it be unusual if the sample mean were greater than $2710? Round answer to at least four decimal places.
(yes/no), because the probability that the sample mean is greater than $2710 is?

Part 5 of 5
(e) Do you think it would be unusual for an individual to have a rent greater than %2710? Explain. Assume the
variable is normally distributed. Round the answer to at least four decimal places.
(yes/no), because the probability that an apartment has a rent greater than $2710 is?

*** PLEASE SHOW HOW TO SOLVE IN EXCEL***

Case Problem 2:        Finding the Best Car Value

(Copy the worksheet named “FamilySedans” in QMB3200-Homework#10Data.xlsx into your file for this problem)

When trying to decide what car to buy, real value is not necessarily determined by how much you spend on the initial purchase. Instead, cars that are reliable and don’t cost much to own often represent the best values. But, no matter how reliable or inexpensive a car may cost to own, it must also perform well. To measure value, Consumer Reports developed a statistic referred to as a value score. The value score is based upon five-year owner costs, overall road-test scores, and predicted reliability ratings. Five-year owner costs are based on the expenses incurred in the first five years of ownership, including depreciation, fuel, maintenance and repairs, and so on. Using a national average of 12,000 miles per year, an average cost per mile driven is used as the measure of five-year owner costs. Road-test scores are the results of more than 50 tests and evaluations and are based upon a 100-point scale, with higher scores indicating better performance, comfort, convenience, and fuel economy. The highest road-test score obtained in the tests conducted by Consumer Reports was a 99 for a Lexus LS 460L. Predicted-reliability ratings (1 = Poor, 2 = Fair, 3 = Good, 4 = Very Good, and 5 = Excellent) are based on data from Consumer Reports’ Annual Auto Survey.

A car with a value score of 1.0 is considered to be “average-value.” A car with a value score of 2.0 is considered to be twice as good a value as a car with a value score of 1.0; a car with a value score of 0.5 is considered half as good as average; and so on. The data for 20 family sedans, including the price ($) of each car tested are contained in the worksheet “FamilySedans.”

Managerial Report

1. Develop numerical summaries of the data.
2. Use regression analysis to develop an estimated regression equation that could be used to predict the value score given the price of the car.
3. Use regression analysis to develop an estimated regression equation that could be used to predict the value score given the five-year owner costs (cost/mile).
4. Use regression analysis to develop an estimated regression equation that could be used to predict the value score given the road-test score.
5. Use regression analysis to develop an estimated regression equation that could be used to predict the value score given the predicted-reliability

What conclusions can you derive from your analysis?

1.A ______________________ provides additional information about variability. a.Point estimate b.Confidence estimate c.Confidence interval d.Point interval

2. ________________________ is the amount added and subtracted to the point estimate to form the confidence interval. a.Standard error b.Sampling error c.Sampling mean d.Margin of error

3. A sample of 36 sheets of metal from a large normal population has a mean thickness of 30 mm. We know from previous quality control testing that the population standard deviation is 3.3 mm. Develop a 95% confidence interval for the true mean for the population.

4. A random sample of 16 people has a mean age = 40 years old and a sample standard deviation of 5 years. Form an 80% confidence interval for the mean.

1. A random sample of 100 people in Lawrence shows that 35 are Republicans. Form a 95% confidence interval for the true proportion of Republicans.

2. If the historical proportion (π) = .7 what is the sample size necessary to have a large enough sample?

3. ____________ measures the strength of the linear association between two variables

1. Correlation
2. Regression
3. Confidence interval
4. Strength test
5. Scatter diagram

1. Statistics are used to infer something about the __________________.

2.A population has mean μ = 19 and standard deviation σ = 5. A random sample of size n = 64 is selected. What is the probability that the sample mean is less than 18?

3.A population has mean μ = 16 and standard deviation σ = 2.0. A random sample of size n = 36 is selected. What is the probability that the sample mean is greater than 16.8?

4.The proportion of students that have taken the census is π = .7, what is the probability that a sample of size 50 yields a sample proportion of .75

a) Why are repeated measures designs more powerful than between subjects designs? Mention the error term.

b) If you were to compute a repeated measures ANOVA as a between subjects ANOVA how would the results differ?

In a random sample of 200 people, 135 said that they watched educational TV. Find the 95% confidence interval of the true proportion of people who watched educational TV.

• A.

  0.325 <  < 0.675

• B.

  –1.96 <  < 1.96

• C.

  0.6101 <  <  0.7399

• D.

  0.6704 < < 0.6796

You work for a marketing firm that has a large client in the automobile industry. You have been asked to estimate the proportion of households in Chicago that have two or more vehicles. You have been assigned to gather a random sample that could be used to estimate this proportion to within a 0.035 margin of error at a 95% level of confidence

. a) With no prior research, what sample size should you gather in order to obtain a 0.035 margin of error?

b) Your firm has decided that your plan is too expensive, and they wish to reduce the sample size required. You conduct a small preliminary sample, and you obtain a sample proportion of ˆ p = 0.19 . Using this new information. what sample size should you gather in order to obtain a 0.035 margin of error?

(a) Holding all other values constant, increasing the sample size increases the power of a hypothesis test. (True/False)

(b) If a 95% confidence interval (CI) for μ is (52, 58), then 95% of the population values are between 52 and 58. (True/False)

(c) If the population distribution (X dist.) is normal, then the sampling distribution of X̅ is normal for a random sample of
any size. (True/False)

(d) A 95% confidence interval for μ was computed to be (30, 35). The margin of error equals 5. (True/False)

(e) If the null hypothesis is not rejected, there is strong evidence that the null hypothesis is true. (True/False)

(f) Holding all other values constant, decreasing alpha (α) increases the power of a hypothesis test. (True/False)

(g)If samples are selected from the same population, the quantities X̅ and S will vary from sample to sample. (True/False)

Suppose there is a rope company that produces rope by the bundle. The length of a bundle (in meters) is a random variable X~N(50,0.2). Calculate the following probabilities.

A.) The length of the bundle is less than 50.19 m

B.) the length of the bundle is greater than 50.16 m

C.) The length of the coil is between 50.16 m and 50.19 m

D.) Determine the positive number a such that p (50-a ≤ X ≤ 50 + a) = 0.9. Interpret the result.

A small university knows the average amount that its students spend on lunch each day. The amount spent on lunches for the population of 500 students is not highly skewed and has a mean of $8 and a standard deviation of $2. Suppose simple random sample of 49 students is taken, what is the probability that the sample mean for the sample of 49 students will be between $7.50 and $8.50?

For the following, Use the five-step approach to hypothesis testing found on page 8-16. It states. You can use excel to compute the data or you can do it by hand. The YouTube videos provided in the links will walk you through the steps to complete the following problems.

1. State the hypothesis and identify the claim.

H0:

H1:

2. Find the critical value and determine what error level to use. For all the problems on this homework use an alpha level of .05 Determine if the test is directional or non-directional.
3. Compute the test Value for the student t-test
4. Make a decision to reject or fail to reject the null hypothesis.
5. Summarize the results

Problem #1 you have eight students who you randomly assign to a treatment group in a chemistry class that received a new method of instruction (Motivational Instruction). You randomly assign eight students from a chemistry class that did not receive the new method of instruction. You want to determine if a new method of instruction has an effect on final semester grades. You want to determine if the final grade scores are higher for the treatment group than they are for the group that did not receive the new instruction method. The data are as follows: using the five-step approach and the data provided complete the five steps. You will use a t-test for independent groups with an alpha level of .05 report the P value as well.

Group 1          Group 2

67                     88

72                     92

80                     78

57                     82

81                     97

71                    100

65                     90

74                     88

Bonus: Worth 10 extra points and must answer both parts to receive the bonus. What are the independent and dependent variables in this research project?

According to an​ airline, flights on a certain route are on time 80​% of the time. Suppose 11 flights are randomly selected and the number of​ on-time flights is recorded. ​ ​(a) Determine the values of n and p. ​(b) Find and interpret the probability that exactly 9 flights are on time. ​(c) Find and interpret the probability that fewer than 9 flights are on time. ​(d) Find and interpret the probability that at least 9 flights are on time. ​(e) Find and interpret the probability that between 7 and 9 ​flights, inclusive, are on time.