Thirty-four small communities in Connecticut (population near 10,000 each) gave an average of x = 138.5 reported cases of larceny per year. Assume that σ is known to be 41.7 cases per year.

(a) Find a 90% confidence interval for the population mean annual number of reported larceny cases in such communities. What is the margin of error? (Round your answers to one decimal place.)

(b) Find a 95% confidence interval for the population mean annual number of reported larceny cases in such communities. What is the margin of error? (Round your answers to one decimal place.)

(c) Find a 99% confidence interval for the population mean annual number of reported larceny cases in such communities. What is the margin of error? (Round your answers to one decimal place.)

(d) Compare the margins of error for parts (a) through (c). As the confidence levels increase, do the margins of error increase?

As the confidence level increases, the margin of error decreases.

As the confidence level increases, the margin of error remains the same.     

As the confidence level increases, the margin of error increases.

(e) Compare the lengths of the confidence intervals for parts (a) through (c). As the confidence levels increase, do the confidence intervals increase in length?

As the confidence level increases, the confidence interval increases in length.

As the confidence level increases, the confidence interval remains the same length.     

As the confidence level increases, the confidence interval decreases in length.

An investment analyst has tracked a certain fund and found that it moves independently day to day, up or down a point. The probability of going up is 75%. What is the probability that four days from now, the price will be the same as now?

A worldwide organization of academics claims that the mean IQ score of its members is 118, with a standard deviation of 16. A randomly selected group of 40 members of this organization is tested, and the results reveal that the mean IQ score in this sample is 115.8. If the organization's claim is correct, what is the probability of having a sample mean of 115.8 or less for a random sample of this size? Carry your intermediate computations to at least four decimal places. Round your answer to at least three decimal places.

A Monte Carlo simulation is a method for finding a value that is difficult to compute by performing many random experiments.

For example, suppose we wanted to estimate π to within a certain accuracy. We could do so by randomly (and independently) sampling n points from the unit square and counting how many of them are inside the unit circle (assuming that the probability of selecting a point in a given region is proportional to the area of the region). By assuming we actually get the expected number, we can solve for π.

(a) Describe a reasonable sample space to model this experiment.

(b) Let N be the number of sample points that are inside the unit circle. Find E(N).

(c) Use this to construct a random variable P with E(P) = π. This random variable will give your estimate of π.

(d) Find the variance of P.

(e) Use Chebychev’s inequality to find a value of n that guarantees your estimate is within 1/1000 of π with probability at least 50%.

The following table shows ceremonial ranking and type of pottery sherd for a random sample of 434 sherds at an archaeological location.

Use a chi-square test to determine if ceremonial ranking and pottery type are independent at the 0.05 level of significance.

(a) What is the level of significance?


State the null and alternate hypotheses.

H₀: Ceremonial ranking and pottery type are not independent. H₁: Ceremonial ranking and pottery type are not independent.

H₀: Ceremonial ranking and pottery type are independent.   H₁: Ceremonial ranking and pottery type are not independent.    

H₀: Ceremonial ranking and pottery type are independent.   H₁: Ceremonial ranking and pottery type are independent.

H₀: Ceremonial ranking and pottery type are not independent.   H₁: Ceremonial ranking and pottery type are independent.

(b) Find the value of the chi-square statistic for the sample. (Round the expected frequencies to at least three decimal places. Round the test statistic to three decimal places.)


Are all the expected frequencies greater than 5?

Yes No    

What sampling distribution will you use?

Student's t

chi-square    

binomial

uniform

normal

What are the degrees of freedom?


(c) Find or estimate the P-value of the sample test statistic. (Round your answer to three decimal places.)


(d) Based on your answers in parts (a) to (c), will you reject or fail to reject the null hypothesis of independence?

Since the P-value > α, we fail to reject the null hypothesis.Since the P-value > α, we reject the null hypothesis.    

Since the P-value ≤ α, we reject the null hypothesis.Since the P-value ≤ α, we fail to reject the null hypothesis.

(e) Interpret your conclusion in the context of the application.

At the 5% level of significance, there is sufficient evidence to conclude that ceremonial ranking and pottery type are not independent.

At the 5% level of significance, there is insufficient evidence to conclude that ceremonial ranking and pottery type are not independent.    

The accompanying table shows a portion of data consisting of the selling price, the age, and the mileage for 20 used sedans. PictureClick here for the Excel Data File Selling Price Age Miles 13,554 7 61,477 13,713 8 54,368 22,970 2 8,242 15,260 2 24,882 16,386 1 22,126 16,639 7 23,654 16,902 2 47,397 18,485 3 16,820 18,830 7 35,376 19,828 3 29,634 11,896 8 55,775 14,937 6 46,198 15,879 3 37,035 16,467 7 45,548 9,478 8 86,924 12,994 6 77,257 15,710 7 59,600 10,517 9 93,215 8,940 10 48,217 11,953 10 42,411 a. Determine the sample regression equation that enables us to predict the price of a sedan on the basis of its age and mileage. (Negative values should be indicated by a minus sign. Round your answer to 2 decimal places.) Priceˆ = + Age + Miles. b. Interpret the slope coefficient of Age. The slope coefficient of Age is −487.30, which suggests that for every additional year of age, the predicted price of car decreases by $487.30. The slope coefficient of Age is −0.08, which suggests that for every additional year of age, the predicted price of car decreases by $0.08. The slope coefficient of Age is −487.30, which suggests that for every additional year of age, the predicted price of car decreases by $487.30, holding number of miles constant. The slope coefficient of Age is −0.08, which suggests that for every additional year of age, the predicted price of car decreases by $0.08, holding number of miles constant. c. Predict the selling price of a eight-year-old sedan with 68,000 miles. (Round intermediate calculations to at least 4 decimal places and final answer to 2 decimal places.) Priceˆ = $

A doctor finds that there is a positive correlation between the amount of hours slept and memory performance. What is the best way to show the results?

Group of answer choices

a.scatterplots

b.line graphs

c.bar graphs

d.pie charts

We wish to look at the relationship between y and x. Summary measures are given below:

n=5, SS_xx=137.2, SS_yy=242.8, and SS_xy=-169.4

Find the t test statistic for the hypothesis H₀: β₁=0 vs H_a: β₁≠0.

Please give detailed explanation

Test the hypothesis that the average number of T.Vs in U.S. households is less than 3. Your sample consists of 100 households with a mean of 2.84 T.Vs. You know the population standard deviation to be 0.8. Your desire a level of significance of 0.05

CASE STUDY
ALABAMA AIRLINE’S CALL CENTER
Alabama Airlines opened its doors in December 2001 as a commuter service with its
headquarters and hub located in Birmingham. The airline was started and managed by two
former pilots, David Douglas and George Devenney. It acquired a fleet of 12 used prop-jet
planes and the airport gates vacated by Delta Air Line’s 2001 downsizing due to September 11
terrorist attacks.
Table 1. Incoming Call Distribution
Time Between Calls (minutes) Probability
1 .11
2 .21
3 .22
4 .20
5 .16
6 .10
With business growing quickly, Douglas turned his attention to Alabama Air’s “800”
reservations system. Between midnight and 6:00 A. M., only one telephone reservations agent
had been on duty. The time between incoming calls during this period is distributed as shown in
Table 1. Carefully observing and timing the agent, Douglas estimated that the time required to
process passenger inquiries is distributed as shown in Table 2.
Table 2. Service-Time Distribution
Time to Process Customer Inquiries (minutes) Probability
1 .20
2 .19
3 .18
4 .17
5 .13
6 .10
7 .03
All customers calling Alabama Air go “on hold” and are served in the order of the calls received
unless the reservations agent is available for immediate service. Douglas is deciding whether a
second agent should be on duty to cope with customer demand. To maintain customer
satisfaction, Alabama Air wants a customer to be “on hold” for no more than 3 to 4 minutes; it
also wants to maintain a “high” operator utilization.
Furthermore, the airline is planning a new TV advertising campaign. As a result, it expects an
increase in “800” line phone inquiries. Based on similar campaigns in the past, the incoming call
distribution from midnight to 6:00 A. M. is expected to be as shown in Table 3. (The same service-time distribution will apply.)

Table 3. Incoming Call Distribution
Time Between Calls (minutes) Probability
1 .22
2 .25
3 .19
4 .15
5 .12
6 .07

Discussion Questions
1. Given the original call distribution, what would you advise Alabama Air to do for the
current reservation system? Create a simulation model to investigate the scenario.
Describe the model carefully and justify the duration of the simulation, assumptions, and
measures of performance.
2. What are your recommendations regarding operator utilization and customer satisfaction
if the airline proceeds with the advertising campaign?

Discussion Questions
1. Given the original call distribution, what would you advise Alabama Air to do for the
current reservation system? Create a simulation model to investigate the scenario.
Describe the model carefully and justify the duration of the simulation, assumptions, and
measures of performance.
2. What are your recommendations regarding operator utilization and customer satisfaction
if the airline proceeds with the advertising campaign?

1. You take a sample of 4 people’s scores on a personality test. Their scores are 13, 16, 12, and 18. You don’t know the population mean or standard deviation. The mean of these scores is 14.75.

1. Use the corrected standard deviation formula to find the population standard deviation. Round to 2 decimal places. (Hint: Draw the chart)

2. Use the population standard deviation from (a) to find the standard error for these for sample. Round to 2 decimal places.

The accompanying data file contains 20 observations for t and y_t.

b-1. Estimate a linear trend model and a quadratic trend model. (Negative values should be indicated by a minus sign. Round your answers to 2 decimal places.)

b-2. Which trend model describes the data well?

• Linear trend based on the R² measure.

• Linear trend based on the adjusted R² measure.

• Quadratic trend based on the R² measure.

• Quadratic trend based on the adjusted R-squared and P-value for the quadratic term

Explain the different hypothesis tests one could use when assessing the distribution of a categorical variable (e.g. smoking status) with only two levels (e.g. levels: smoker and non-smoker) vs. more than two levels (e.g. levels: heavy smoker, moderate smoker, occasional smoker, non-smoker).

Be precise. Use the language of the textbook to identify the appropriate test and how you would conduct it. NOTE: Minimum of 150 words for primary post and 50 words for each of three replies to your peers.