A research center survey of 2 comma 375 adults found that 1 comma 942 had bought something online. Of these online​ shoppers, 1 comma 274 are weekly online shoppers. Complete parts​ (a) through​ (c) below.

1. Construct a​ 95% confidence interval estimate of the population proportion of adults who had bought something online.
2. Construct a​ 95% confidence interval estimate of the population proportion of online shoppers who are weekly online shoppers.
3. How would the director of​ e-commerce sales for a company compare the results of​ (a) and​ (b)?

The therm dataset contains information on survey respondents’ opinions about various public figures. These are “feeling thermometer” scores, which range from 0 (total dislike of the person) to 100 (total like). The relevant variables for this question are:

• white: a dummy variable indicating whether the respondent is white (ie, 1 for white and 0 for non-white)

• ideology: the respondent’s ideology on a scale of 1 (most liberal) to 7 (most conservative)

• obama: the respondent’s “feeling thermometer” score for Barack Obama

(a) One regression with obama as the dependent variable and white and ideology as the independent variables shows that

obama = 111.2 − 21.2 ∗ white − 8.7 ∗ ideology

What is the estimated intercept for white respondents? What about for non-white respondents?

(b) Another regression that includes a term for the interaction between white and ideology shows that

obama = 90.3+ 8.3∗white−3.0∗ideology−7.6∗(white ·ideology)

What are the estimated intercept and slope of ideology among white respondents? What about among non-white respondents? Is the relationship between ideology and Obama opinion stronger for white respondents, or non-white respondents?

1. An ecologist is interested in studying the presence of different types of animal species in different locations. Using the following contingency table and the total sample size, rewrite the frequencies as relative frequencies. Round each relative frequency to two decimal places.

2. You are interested in learning about students' favorite mode of transportation at two universities. Fill in the blanks in the following contingency table, assuming that the variables are independent.

3.Your teacher claims that the final grades in class are distributed as: A, 25%; B, 25%; C, 40%; D, 5%; F, 5%. At the end of a randomly selected academic quarter, the following number of grades are recorded. Calculate the appropriate chi-square test statistic that would be used to determine if the grade distribution for the course is different than expected. Round your answer to two decimal places.

4. A dog breeder wishes to see if prospective dog owners have any preference among six different breeds of dog. A sample of 200 people (prospective dog owners) provided the data below. Find the critical chi-square value that would be used to test the claim that the distribution is uniform. Use α = 0.01 and round your answer to three decimal places.

Calcium levels in people are normally distributed with a mean of 9.7mg/dL and a standard deviation of 0.3mg/dL. Individuals with calcium levels in the bottom 15

% of the population are considered to have low calcium levels. Find the calcium level that is the borderline between low calcium levels and those not considered low. Carry your intermediate computations to at least four decimal places. Round your answer to one decimal place.Calcium levels in people are normally distributed with a mean of

9.7mg/dL and a standard deviation of 0.3mg/dL. Individuals with calcium levels in the bottom 15% of the population are considered to have low calcium levels. Find the calcium level that is the borderline between low calcium levels and those not considered low. Carry your intermediate computations to at least four decimal places. Round your answer to one decimal place.

A recent study found that children who watched a cartoon with food advertising​ ate, on​ average, 28.6 grams of crackers as compared to an average of 18.8 grams of crackers for children who watched a cartoon without food advertising. Suppose that there were 61 children in each​ group, and the sample standard deviation for those children who watched the food ad was 8.7 grams and the sample standard deviation for those children who did not watch the food ad was 7.7 grams. Complete parts​ (a) and​ (b) below.

b. Assuming that the population variances are​ equal, construct 95% confidence interval estimate of the difference μ1−μ2 between the mean amount of crackers eaten by the children who watch and do not watch the food ad.

___≤ μ1−μ2 ≤ ___ (Round to two decimal places as needed.)

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