A national television network took an exit poll of 1460 voters after each had cast a vote in a state gubernatorial election. Of​ them, 680 said they voted for the RepublicanRepublican candidate and 780 said they voted for the DemocraticDemocratic candidate. Treating the sample as a random sample from the population of all​ voters, a 95​% confidence interval for the proportion of all voters voting for the DemocraticDemocratic candidate was (0.509, 0.560). Suppose the same proportions resulted from n=146146 ​(instead of 146​), with counts of 68 and 78​, and that there are only two candidates. Complete parts a and b below.

a. Does a 95% confidence interval using the smaller sample size allow you to predict the​ winner? Explain.

The 95​% confidence interval for the proportion of all voters voting for the DemocraticDemocratic candidate is (____, _____). Now a 95​% confidence interval (does, does not) allow you to predict the​ winner, since this interval (does not include, includes) (0,1, or 0.5).

Problem 12-15 (Algorithmic)

Strassel Investors buys real estate, develops it, and resells it for a profit. A new property is available, and Bud Strassel, the president and owner of Strassel Investors, believes if he purchases and develops this property it can then be sold for $170000. The current property owner has asked for bids and stated that the property will be sold for the highest bid in excess of $100000. Two competitors will be submitting bids for the property. Strassel does not know what the competitors will bid, but he assumes for planning purposes that the amount bid by each competitor will be uniformly distributed between $100000 and $150000.

1. Develop a worksheet that can be used to simulate the bids made by the two competitors. Strassel is considering a bid of $120000 for the property. Using a simulation of 1000 trials, what is the estimate of the probability Strassel will be able to obtain the property using a bid of $120000? Round your answer to 1 decimal place. Enter your answer as a percent.
   
   %
   
2. How much does Strassel need to bid to be assured of obtaining the property?
   
   $  
   
   What is the profit associated with this bid?
   
   $  
   
3. Use the simulation model to compute the profit for each trial of the simulation run. With maximization of profit as Strassel’s objective, use simulation to evaluate Strassel’s bid alternatives of $120000, $145000, or $150000. What is the recommended bid, and what is the expected profit?
   
   A bid of $145000  results in the largest mean profit of $  .

You are hired by Google to research how much people are willing to pay for a new cell phone in US. They are especially interested to know if their new phone, Pixel 3, should be priced similarly to Apple’s iPhone Xs. Google believes that there is a difference between what Android and iPhone users are willing to pay for high-end phones. You are hired to answer this question. Part I: To analyze iPhone users your team randomly selects 16 individuals. See attached data file.

a) Compute sample mean and sample standard deviation for iPhone users

b) Compute 5-number summary for iPhone users

c) Find the 90% confidence interval for the average phone price iPhone users are willing to pay. How do you interpret it?

Use Excel to develop a multiple regression model to predict Cost of Materials by Number of Employees, New Capital Expenditures, Value Added by Manufacture, and End-of-Year Inventories.

Locate the observed value that is in Industrial Group 12 and has 7 employees. Based on the model and the multiple regression output, what is the corresponding residual of this observation? Write your answer as a number, round to 2 decimal places.

Problem 12-01

The management of Brinkley Corporation is interested in using simulation to estimate the profit per unit for a new product. The selling price for the product will be $45 per unit. Probability distributions for the purchase cost, the labor cost, and the transportation cost are estimated as follows:

1. Compute profit per unit for the base-case, worst-case, and best-case scenarios.
   
   Profit per unit for the base-case: $  
   
   Profit per unit for the worst-case: $  
   
   Profit per unit for the best-case: $  
   
2. Construct a simulation model to estimate the mean profit per unit. If required, round your answer to the nearest cent.
   
   Mean profit per unit = $  
   
3. Why is the simulation approach to risk analysis preferable to generating a variety of what-if scenarios?
   
   The input in the box below will not be graded, but may be reviewed and considered by your instructor.
   
   
   
4. Management believes the project may not be sustainable if the profit per unit is less than $5. Use simulation to estimate the probability the profit per unit will be less than $5. If required, round your answer to two decimal places.
   
   %

The following is a cross-tabulation of the variables gender and units (the number of units in which a student has enrolled) from a recent class survey. Number of Units Gender 1 2 3 4 5 female 4 11 60 191 3 male 2 10 28 86 1 Note that χ 2 tests require all expected frequencies to be at least 5. To ensure this you may need to combine columns in a way that makes sense in the context of a test for association. That is, you could combine columns 1 and 2, but not columns 1 and 4. Assuming the data come from randomly-selected Murdoch University students, test for an association between gender and unit load in the Murdoch University student population. If you find an association, describe it.

A researcher wants to study the relationship between salary and gender. She randomly selects 330 ... A researcher wants to study the relationship between salary and gender. She randomly selects 330 individuals and determines their salary and gender. Can the researcher conclude that salary and gender are dependent?

Income Male Female Total

Below $25,000 25 16 41

$25,000-$50,000 47 103 150

$50,000-$75,000 48 32 80

Above $75,000 36 23 59

Total 156 174 330

Step 1 of 8: State the null and alternative hypothesis. Step 2 of 8: Find the expected value for the number of men with an income below $25,000. Round your answer to one decimal place. Step 3 of 8: Find the expected value for the number of men with an income $50,000-$75,000. Round your answer to one decimal place. Step 4 of 8: Find the value of the test statistic. Round your answer to three decimal places. Step 5 of 8: Find the degrees of freedom associated with the test statistic for this problem. Step 6 of 8: Find the critical value of the test at the 0.01 level of significance. Round your answer to three decimal places. Step 7 of 8: Make the decision to reject or fail to reject the null hypothesis at the 0.01 level of significance. Step 8 of 8: State the conclusion of the hypothesis test at the 0.01 level of significance.

a hospital administrator wants to estimate the mean length of stay for all inpatients in the hospital. Based on a random sample of 676 patients from the previous year, she finds that the sample mean is 5.3 days with a standard deviation of 1.2 days. Construct and interpret a 95% and a 99% confidence interval for the mean.

1. I am interested in asking people what they think about the current election and who their favorite candiate is. I decide to go to random subdivisons and city blocks and ask 15 people from each region who their favorite candiate is. I decide to go to random subdivisons and city blocks and ask 15 people from each region who their favorite candiate is. This is an example of:

a. Stratified sampling

b. Simple Random Sampling

c. Systematic Sampling.

d. Cluster Sampling

2. If we have two unbiased estimators, the next thing we are interested in checking is if they are:

a. Efficient

b. Consistent

3. 77% Of people have a gpa of 3.0 or higher. Suppose we take a random sample of 500 students.

a. What is the standard error of the proportion

b. What is the probabilty that 80% or more of those people will have a gpa higher than 3.0

4. In 2010, the average finshing time for marathons across the US was approximately 278 minutes, with a standard deviation of approximately 63 minutes. what finishing time defines the fastes 7.93% of runners?

a. 366.83

b. 189.17

c. 348.76

d. 405.78

Part 1: The following numbers below represent heights (in feet) of 3-year old elm trees: 5.1, 5.8, 6.1, 6.2, 6.4, 6.7, 6.8, 6.9, 7.0, 7.2, 7.3, 7.3, 7.4, 7.5, 8.1, 8.1, 8.2, 8.3, 8.5, 8.6, 8.6, 8.7, 8.7, 8.9, 8.9, 9.0, 9.1, 9.3, 9.4. Assuming that the heights of 3-year old elm trees are normally distributed, find a (two-sided) 90% confidence interval for the mean height of 3-year old elm trees.

Part 2:Assuming that the heights of 3-year old elm trees are normally distributed, use the data in the previous problem to test whether the average height of 3-year old elm trees is greater than 7.5 feet, at significance level 0.05. Also, what is the p-value of the test?

3) When I lived in California I had a small lemon tree in the front yard. If we had rain in the summer (rare=P=.2) it would yield up to 10 lemons, distributed with a binomial distribution, N= 10, P=0.6. If it is perfectly dry (most of the time P=0.8) it the distribution would be binomial with N=6, P=0.4 a) If you get 3 lemons what the probability that it rained. b) If you have 4 lemons, what is the probability that it rained.

2. A firm is considering the delivery times of two raw material suppliers, A and B. The firm is basically satisfied with supplier A; however, if the firm finds the mean delivery time of supplier B is less than the mean delivery time of supplier A, the firm will begin purchasing raw materials from supplier B (meaning, switch from supplier A to supplier B). Independent samples (assume equal population variances) show the following sample data for the delivery times of the two suppliers:

a. State the null and alternative hypotheses for this situation.
b. Describe what a Type I Error would be in this situation (please be as specific as possible).
c. If α = 0.01, what is the critical value of the associated test statistic?
d. What is the calculated value of the associated test statistic?
e. State your decision about the null hypothesis by comparing the critical and calculated values of the test statistic (Parts c and d).
f. What action do you recommend in terms of supplier selection?

4. For this problem, you’ll compare the hypergeometric and binomial distributions. Suppose there is a sock drawer with N socks, each placed loosely in the drawer (not rolled into pairs). The total number of black socks is m. You take out a random sample of n < m socks. Assume all the socks are the same shape, size, etc. and that each sock is equally likely to be chosen.

(a) Suppose the sampling is done without replacement. Calculate the probability of getting at least 2 black socks (your goal in order to wear matching black socks that day...) under the following conditions:

(i) N = 10, n = 4, m = 5.

(ii) N = 20, n = 4, m = 10.

(iii) N = 40, n = 4, m = 20.

(b) Suppose the sampling is done with replacement (this doesn’t make much sense if you are planning to wear the socks!). Calculate the probability of getting at least two black socks when you sample four socks and the proportion of black socks is 0.5. Compare your answer to those in (a).

7. The mean weekly earnings for employees in general automotive repair shops is $450 and the standard deviation is $50. A sample of 100 automotive repair employees is selected at random.
a. Find the probability that the mean earnings is less than $445.

b. Find the probability that the mean earning is between $445 and $455.

c.Find the probability that the mean earnings is greater than $460.

8. A drug manufacturer states that only 5% of the patients using a high blood pressure drug will experience side effects. Doctors at a large university hospital use the drug in treating 200 patients.
a.What is the probability that 15 or fewer patients will experience a side effect?

b. What is the probability that between 7 and 12 patients will experience a side effect?