In the Excel file Restaurant Sales, determine if the variance of weekday (M/T/W/T/F) sales is different from that of weekend (S/S) sales with significance level of 5% for the variable delivery sales.

The Arkansas Western Gas Company (AWGC) recently filed a rate increase request with the public service commission. The rate increase was calculated based on a mean consumption of 6400 cubic feet of natural gas per month per customer. In order to check this usage figure, the Arkansas attorney general’s office obtained a random sample of 21 AWGC customers and recorded the monthly usage for each. The sample mean was 6575 ft3. Assume that the distribution of natural gas consumption is normal with σ = 450. Conduct a one-sided, right-tailed hypothesis test with α = 0.05 and compute the p-value. Is there any evidence to suggest that the true mean usage is greater than 6400 ft3?

Registrar’s Office members design a study of students’ performance. They believe that individual course grades measured in a 100-point scale are normally distributed with the population standard deviation = sigma = 19 points. The goal is to estimate the population mean with the interval no wider than 9 points.

1. Set confidence level = C = 0.99 and find the smallest number of records required for the study goals.

2. Will a sample of n = 100 records guarantee that the interval is no wider than 9 points? Explain your answer.

3. Using confidence level = C = 0.95, find the smallest number of records required for this study.

4. Will the sample of n = 81 guarantee that the interval is no wider than 9 points? Explain your answer.

1. Under coverage is a problem that occurs in surveys when some groups in the population are underrepresented in the sampling frame used to select the sample.  We can check for under coverage by comparing the sample with known facts about the population.
   1. Suppose we take an SRS of n = 500 people from a population that is 25% Hispanic.  How many Hispanics are expected in a given sample? 125
   2. What is the standard deviation for the number of Hispanics in a sample? 9.682
   3. Can the normal approximation to the binomial be used to help make probabilistic statements about samples from this population? The normal approximation to the binomial can be used to help make probabilistic statements about samples about this population because npq (93.75) is greater than 5 which is what is needed in order to make probabilistic statements.
   4. Would a sample mean with 100 Hispanic people be different from the population mean?  Give the p-value and explain your reasoning.
   5. What is the confidence interval for the sample mean of 100?
   6. Does the confidence interval agree with your p-value, explain your reasoning.
   7. Would you suspect undercoverage in a sample with 100 Hispanics?  Explain your reasoning.

Exhibit 3

The amount of time the car has to wait at a particular stoplight is normally distributed with the mean and the standard deviation of 61 seconds and 9 seconds, respectively. A random sample of 25 cars passing through this stoplight was taken.

Question 14

Refer to Exhibit 3. What is the probability that the next car has to wait more than 36 seconds but less than 52 seconds at the stoplight? (Round to the nearest four decimal place.

Question 15

Refer to Exhibit 3. 61.9 percent of the cars has to wait at most X seconds before the stoplight change to green. What is the value of X? (Round to the nearest four decimal place.

Question 16

Refer to Exhibit 3. What is the probability that the random sample of 25 cars mentioned in the Exhibit has a mean waiting time more than 56 seconds? (Round to the nearest four decimal place.)

Part 1 Select the appropriate discrete probability distribution. If using a binomial distribution, use the constant probability from the collected data and assume a fixed number of events of 20. If using a Poisson distribution, use the applicable mean from the collected data. art 2 Using the mean and standard deviation for the continuous data, identify the applicable values of X for the following: Identify the value of X of 20% of the data, identify the value of X for the top 10% of the data, and 95% of the data lies between two values of X.

Mean 4.84 Median 4

Standard Deviation 3.161645141 Sample Variance 9.996

Data

1.5

1.2

2.3

2.7

3.5

4.5

6

7.8

9.4

9.5

What are some of the available commands that can be utilized in R for carrying out a one-sample and two-sample t-test? What are the differences between carrying out a t-test with equal and unequal variance? Please provide an example to illustrate your assertions.

-Find the linear correlation coefficient. (Enter a number. Round your answer to four decimal places.)

R=

-Find the least-squares regression for these data where speed is the independent variable, x, and pulse rate in beats per minute (bpm) is the dependent variable. (Enter a mathematical expression. Round your numerical answers to two decimal places.)

ŷ =

-Assuming the regression line is accurate for higher speeds, what is the expected pulse rate (in bpm) for someone traveling 5 mph? Round to the nearest whole number. (Enter a number.)

An advertisement for a popular supermarket chain claims that it has had consistently lower prices than four other full-service supermarkets. As part of a survey conducted by an "independent market basket price-checking company," the average weekly total, based on the prices (in $) of approximately 95 items, is given for two different supermarket chains recorded during 4 consecutive weeks in a particular month.

Week Advertiser ($) Competitor ($)

1. 254.19 256.00

2 240.66 255.59

3. 231.96 255.20

4 234.04 261.27

(a) Is there a significant difference in the average prices for these two different supermarket chains? (Use α = 0.05. Round your answers to three decimal places.)

test statistic=

t > =

t < =

(b) Construct a 99% confidence interval for the difference in the average prices for the two supermarket chains. (Round your answers to two decimal places.)

110. A study in transportation safety collected data on 42 North American cities. From each city, two of the variables recorded were X = percentage of licensed drivers who are under 21 years of age, and Y = the number of fatal accidents per year per 1000 licenses. Below is the output from the data: Parameter Std. Estimate Error T Statistic p-value Intercept -1.59741 0.371671 -4.29792 0.0001 Slope 0.287053 0.0293898 9.76711 Unknown Correlation Coefficient = 0.839387 R-squared = 70.4571 percent Standard error of estimate = 0.58935 35

a) What is the formula for the regression function?

b) Interpret the slope of the regression equation.

c) Construct an 95% interval to predict y when x = 14, and explain what it means in the context of the problem.

d) Advanced question? What is the p value for the slope in this problem? Calculate it and show your work? Based on this analysis, can we conclude that the number of fatal accidents is linearly related to the percentage of licensed drives? Justify your answer showing all work. What is the null and the alternative hypothesis?

1. The health of the bear population in Yellowstone National Park is monitored by periodic measurements taken from anesthetized bears. A sample of n = 54 bears has a mean weight of ¯x = 182.9 lb and standard deviation of s = 121.8 lb. 86

(a) Calculate and interpret a 95% confidence interval estimate of the population mean µ bear weight.

(b) Find the length of the confidence interval constructed in part (a).

2. Hemoglobin levels in 11-year-old boys are normally distributed with unknown mean µ and standard deviation = 1.2 g/dL.

(a) Determine the sample size n needed to estimate population mean hemoglobin level with 95% confidence so that the margin of error E = 0.5 g/dL?

(b) Determine the sample size n needed to estimate population mean hemoglobin level with margin of error E = 0.5 g/dL with 99% confidence?

3.  A hospital administrator wished to estimate the average number of days µ
required for treatment of patients between the ages of 25 and 34. A random
sample of n = 35 hospital patients between these ages produced a sample mean
x¯ = 5.4 days and sample standard deviation s = 3.1 days.
(a) Calculate and interpret a 95% confidence interval for the mean length of stay µ for the population of patients from which the sample was drawn.
(b) Determine the length of the interval from part (a).
(c) Calculate and interpret a 99% confidence interval for the mean length of stay µ for the population of patients from which the sample was drawn.
(d) Determine the length of the interval from part (c).
(e) Why is the interval obtained in part (c) wider than that obtained in part (a)?

Spam Spam filters try to sort your e-mails, deciding which are real messages and which are unwanted. One method used is a point system. The filter reads each incoming message and assigns points to the sender, the subject, key words in the message and so on. The higher the point total, the more likely it is that the message is unwanted. The filter has a cutoff value for the point total; any message rated lower than the cutoff passes through to your inbox, and the rest, suspected to be spam, are directed to the junk mailbox. We can think of the filter’s decision as a hypothesis test. The null hypothesis is that the e-mail is a real message and should go to your inbox. A higher point total provides evidence that the message may be spam; when there is sufficient evidence, the filter rejects the null, classifying the message as junk. This ususally works pretty well, but, of course, sometimes the filter makes a mistake. a. (1 mark) When the filter allows spam to slip through into your inbox, which kind of error is that? b. (1 mark) Which kind of error is it when a real message gets classified as junk? c. Some filters allow the user (that’s you) to adjust the cutoff. Suppose your filter has a default cutoff of 50 points, but you reset it to 40. Is that similar to choosing a larger value or similar to choosing a smaller value of α for a hypothesis test? Explain

A random sample of 245 students showed that 189 of them liked listening to music while studying. Find the 90% confidence interval for the proportion of students that like listening to music while studying.

What is the SE (standard error) for this sample?

In a survey of 176 females who recently completed high​ school, 75​% were enrolled in college. In a survey of 180 males who recently completed high​ school, 65​% were enrolled in college. At alpha equals 0.09​, can you reject the claim that there is no difference in the proportion of college enrollees between the two​ groups? Assume the random samples are independent. Complete parts​ (b) through​ (e). ​(b) Find the critical​ value(s) and identify the rejection​ region(s). ​(c) Find the standardized test statistic. ​(d) Decide whether to reject or fail to reject the null hypothesis. ​(e) Interpret the decision in the context of the original claim.

What price do farmers get for their watermelon crops? In the third week of July, a random sample of 40 farming regions gave a sample mean of x = $6.88 per 100 pounds of watermelon. Assume that σ is known to be $1.98 per 100 pounds.

(a) Find a 90% confidence interval for the population mean price (per 100 pounds) that farmers in this region get for their watermelon crop. What is the margin of error? (Round your answers to two decimal places.)

(b) Find the sample size necessary for a 90% confidence level with maximal error of estimate E = 0.25 for the mean price per 100 pounds of watermelon. (Round up to the nearest whole number.)
farming regions

(c) A farm brings 15 tons of watermelon to market. Find a 90% confidence interval for the population mean cash value of this crop. What is the margin of error? Hint: 1 ton is 2000 pounds. (Round your answers to two decimal places.)