4. Below is the amount that a sample of 15 customers spent for lunch ($) at a fast-food restaurant: 7.42 6.29 5.83 6.50 8.34 9.51 7.10 5.90 4.89 6.50 5.52 7.90 8.30 9.60 6.80 Recall the lunch at a fast-food restaurant problem from Assignment 4. Let µ represent the population mean amount spent for lunch ($) at a fast-food restaurant. Previously you calculated the mean and standard deviation of the fifteen sample measurements to be x ̅ = $7.09 and s = $1.406, respectively. Suppose you want to determine if the true value of µ differs from $7.50. Specify the null and alternative hypotheses for this test. Since x ̅ = $7.09 is less than $7.50, a manger wants to reject the null hypothesis. What are the problems with using such a decision rule? Compute the value of the test statistic. Find the approximate p-value of the test or use technology to find the exact p-value. Select a value of α, the probability of a Type I error. What does α represent in the words of the problem. Give the appropriate conclusion, based on the results of parts d and e. What conditions must be satisfied for the test results to be valid? In Assignment 4, you found a 95% confidence interval for µ. Does this interval support your conclusion in part f?

PLEASE SHOW ANSWER WITHOUT USING EXCEL OR ANY SOFTWARE. NEED DETAILED WORKINGS OF THE ANSWER. PLEASE NOTE NO EXCEL

The manager of a computer software company wishes to study the number of hours senior executives by type of industry spend at their desktop computers. The manager selected a sample of five executives from each of three industries. At the .05 significance level, can she conclude there is a difference in the mean number of hours spent per week by industry?

PLEASE SHOW ANSWER WITHOUT USING EXCEL OR ANY SOFTWARE. NEED DETAILED WORKINGS OF THE ANSWER. PLEASE NOTE NO EXCEL

Because of staffing decisions, managers of the Gibson-Marimont Hotel are interested in the variability in the number of rooms occupied per day during a particular season of the year. A sample of 24 days of operation shows a sample mean of 294 rooms occupied per day and a sample standard deviation of 26 rooms.

What is the point estimate of the population variance? 676

Provide a 90% confidence interval estimate of the population variance (to 1 decimal). ( , )

Provide a 90% confidence interval estimate of the population standard deviation (to 1 decimal). ( , )

A cell phone manufacturer claims that the batteries in its latest model provide 20 hours of continuous use. In order to verify this claim, and independent testing firm checks the battery life of 100 phones. They find that the batteries in these 100 phones last an average of 19 hours with a standard deviation of 5 hours. Conduct an appropriate hypothesis test to check whether the results from this sample provide sufficient evidence that the true mean battery life is significantly less than 20 hours.

1. Is this a question about the sample mean or the sample proportion? Explain how you know.

2. What is the most appropriate test, a two-tailed test, a right-tailed test, or a left-tailed test? Explain how you know.

3. State the null and alternative hypotheses. Make sure to use proper notation.

4. Calculate the test statistic. Make sure to show all your computations.

5. Determine the P-value. Make sure to explain how you obtained the value.

f. State the decision about the null hypothesis as well as the conclusion from your hypothesis test in the context of the problem.

QUESTION (please show your work so that I may understand how to do the problem) thanks Before you can calculate your test statistic, you’ll have to calculate the SEM. Use the formula in the book/lecture to calculate the SEM. Put your value below. Remember that you will need to calculate the population standard deviation first (remember to use n rather than n-1 for the population standard deviation calculation). Round your response out to two decimal places, if you give more than two decimal places Canvas may count your answer as wrong Pat is the manager of a real estate group that is part of a larger real estate company. Here are the total number of home sales from 2018 for all the agents at the entire company. 4, 5, 10, 4, 6, 7, 9, 11, 3, 4, 8, 9, 2, 4, 3, 12, 4, 5, 6, 3, 8, 9, 8, 7, 10, 4, 5, 7, 8, 6. Pat wants to know if her own real estate group, which has 4 agents (the sample, in this case), has sold more homes than the rest of the company (the population). Your job is to tell me if these four agents (agents A, B, C, and D) differ in number of home sales from the population (the entire company). Remember that you need to calculate the population standard deviation first! Agent Number of Homes Sold in 2018 A 6 B 7 C 8 D 10

1- State the null hypothesis

Group of answer choices

a-H₀: The sample drawn from the population reflects the population, or M = µ

b-H₀: The sample drawn from the population reflects the population, or M ≠ µ

2- State the alternative hypothesis

Group of answer choices

a-H₁: The sample drawn from the population does not reflect the population, or M ≠ µ

b-H₁: The sample drawn from the population reflects the population, or M = µ

3- Determine the best statistical test to use

Group of answer choices

a-Critical value test

b-Z score test

c-Correlational test

d-one-sample Z test

4-Before you can calculate your test statistic, you’ll have to calculate the SEM. Use the formula in the book/lecture to calculate the SEM. Put your value below. Remember that you will need to calculate the population standard deviation first (remember to use n rather than n-1 for the population standard deviation calculation). Round your response out to two decimal places, if you give more than two decimal places Canvas may count your answer as wrong.

5-Now, Compute the test statistic (Use the formulas in the book / lecture to calculate the correct statistic). Which of the following is the correct value?

Group of answer choices

a-z = 0.171

b-z =1.06

c-z = 3.505

d-z = 1.04

6- The value needed to reject the null hypothesis is ___________.

Group of answer choices

a-1.64

b-1.96

c-3.25

d-2.10

7-Does the obtained value exceed the critical value (that is, is the obtained value larger than the critical value)?

Group of answer choices

a-No

b-Yes

8- Based on your answer to the previous question, the decision is to ____________

Group of answer choices

a-Reject the null hypothesis

b-Fail to reject the null hypothesis

Two plots at Rothamsted Experimental Station were studied for production of wheat straw. For a random sample of years, the annual wheat straw production (in pounds) from one plot was as follows.

Use a calculator to verify that, for this plot, the sample variance is s² ≈ 0.312.

Another random sample of years for a second plot gave the following annual wheat production (in pounds).

Use a calculator to verify that the sample variance for this plot is s² ≈ 0.385.

Test the claim that there is a difference (either way) in the population variance of wheat straw production for these two plots. Use a 5% level of signifcance.

(a) What is the level of significance?

State the null and alternate hypotheses.

H_o: σ₁² = σ₂²; H₁: σ₁² > σ₂²

H_o: σ₁² > σ₂²; H₁: σ₁² = σ₂²

H_o: σ₂² = σ₁²; H₁: σ₂² > σ₁²

H_o: σ₁² = σ₂²; H₁: σ₁² ≠ σ₂²

(b) Find the value of the sample F statistic. (Use 2 decimal places.)


What are the degrees of freedom?

What assumptions are you making about the original distribution?

The populations follow independent normal distributions. We have random samples from each population.

The populations follow dependent normal distributions. We have random samples from each population.    

The populations follow independent normal distributions.

The populations follow independent chi-square distributions. We have random samples from each population.

(c) Find or estimate the P-value of the sample test statistic. (Use 4 decimal places.)

p-value > 0.200

0.100 < p-value < 0.200     

0.050 < p-value < 0.100

0.020 < p-value < 0.050

0.002 < p-value < 0.020

p-value < 0.002

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

At the α = 0.05 level, we reject the null hypothesis and conclude the data are not statistically significant

.At the α = 0.05 level, we reject the null hypothesis and conclude the data are statistically significant.     

At the α = 0.05 level, we fail to reject the null hypothesis and conclude the data are not statistically significant.

At the α = 0.05 level, we fail to reject the null hypothesis and conclude the data are statistically significant.

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

Fail to reject the null hypothesis, there is sufficient evidence that the variance in annual wheat production differs between the two plots.

Reject the null hypothesis, there is insufficient evidence that the variance in annual wheat production differs between the two plots.     

Reject the null hypothesis, there is sufficient evidence that the variance in annual wheat production differs between the two plots.

Fail to reject the null hypothesis, there is insufficient evidence that the variance in annual wheat production differs between the two plots.

assume a normal distribution with a mean of 65 and standard deviation of 14 find P(56<X less than or equal to 68)

A tire company produced a batch of 5 comma 300 tires that includes exactly 260 that are defective. a. If 4 tires are randomly selected for installation on a​ car, what is the probability that they are all​ good? b. If 100 tires are randomly selected for shipment to an​ outlet, what is the probability that they are all​ good? Should this outlet plan to deal with defective tires returned by​ consumers?

Suppose the lengths of the pregnancies of a certain animal are approximately normally distributed with mean mu equals 127 days and standard deviation sigma equals 12 days. Complete parts​ (a) through​ (f) below. ​(a) What is the probability that a randomly selected pregnancy lasts less than 123 ​days? The probability that a randomly selected pregnancy lasts less than 123 days is approximately 0.3694. ​(Round to four decimal places as​ needed.) Interpret this probability. Select the correct choice below and fill in the answer box within your choice. ​(Round to the nearest integer as​ needed.) A. If 100 pregnant individuals were selected independently from this​ population, we would expect 37 pregnancies to last less than 123 days. B. If 100 pregnant individuals were selected independently from this​ population, we would expect nothing pregnancies to last more than 123 days. C. If 100 pregnant individuals were selected independently from this​ population, we would expect nothing pregnancies to last exactly 123 days. ​(b) Suppose a random sample of 20 pregnancies is obtained. Describe the sampling distribution of the sample mean length of pregnancies. The sampling distribution of x overbar is normal with mu Subscript x overbarequals 127 and sigma Subscript x overbarequals 2.9104. ​(Round to four decimal places as​ needed.) ​(c) What is the probability that a random sample of 20 pregnancies has a mean gestation period of 123 days or​ less? The probability that the mean of a random sample of 20 pregnancies is less than 123 days is approximately nothing. ​(Round to four decimal places as​ needed.) Interpret this probability. Select the correct choice below and fill in the answer box within your choice. ​(Round to the nearest integer as​ needed.) A. If 100 independent random samples of size nequals20 pregnancies were obtained from this​ population, we would expect nothing ​sample(s) to have a sample mean of 123 days or less. B. If 100 independent random samples of size nequals20 pregnancies were obtained from this​ population, we would expect nothing ​sample(s) to have a sample mean of 123 days or more. C. If 100 independent random samples of size nequals20 pregnancies were obtained from this​ population, we would expect nothing ​sample(s) to have a sample mean of exactly 123 days. ​(d) What is the probability that a random sample of 39 pregnancies has a mean gestation period of 123 days or​ less? The probability that the mean of a random sample of 39 pregnancies is less than 123 days is approximately nothing. ​(Round to four decimal places as​ needed.) Interpret this probability. Select the correct choice below and fill in the answer box within your choice. ​(Round to the nearest integer as​ needed.) A. If 100 independent random samples of size nequals39 pregnancies were obtained from this​ population, we would expect nothing ​sample(s) to have a sample mean of 123 days or less. B. If 100 independent random samples of size nequals39 pregnancies were obtained from this​ population, we would expect nothing ​sample(s) to have a sample mean of exactly 123 days. C. If 100 independent random samples of size nequals39 pregnancies were obtained from this​ population, we would expect nothing ​sample(s) to have a sample mean of 123 days or more. ​(e) What might you conclude if a random sample of 39 pregnancies resulted in a mean gestation period of 123 days or​ less? This result would be ▼ expected, unusual, so the sample likely came from a population whose mean gestation period is ▼ less than equal to greater than 127 days. ​(f) What is the probability a random sample of size 15 will have a mean gestation period within 12 days of the​ mean? The probability that a random sample of size 15 will have a mean gestation period within 12 days of the mean is nothing. ​(Round to four decimal places as​ needed.)

n Ecological Engineering, the potential for floating aquatic plants to treat dairy manure wastewater was investigated. For one part of the study, 16 treated wastewater samples were randomly divided into two groups- a control algal was cultured in half the samples and the water hyacinth was cultured in the other half. The rate of increase in the amount of total phosphorus was measured in each water sample. The control algal had a sample mean of 0.036 with a standard deviation of 0.008 while the water hyacinth had a sample mean of 0.026 with a standard deviation of 0.006. Conduct a test to determine if there is a difference in mean rates of increase of total phosphorus for the two aquatic plants. Use alpha = 0.05.

1) What type of test should be conducted?

The town of Pleasantville is going to form a public safety committee. Pleasantville already has a seven-person town council, a five-person citizen advisory board; the police force is made up of ten officers. There is no overlap between the members of the town council, the citizen advisory board, and the police force.
Express all probabilities as decimals, rounded to six places.

14) If the committee must include three members from the town council, two members from the citizen advisory board, and three members from the police force, how many different ways can the committee be formed?

b) Suppose the public safety committee is made up as described in #14, and members are to be chosen at random from each of the town council, advisory board, and police force. If Tayler is on the town council, what is the probability they will be selected for the committee?

c) Suppose the public safety committee is made up as described in #14, and members are to be chosen at random from each of the town council, advisory board, and police force. If Casey is on the citizen advisory board, what is the probability they will be selected for the committee?

d) Suppose the public safety committee is made up as described in #14, and members are to be chosen at random from each of the town council, advisory board, and police force. If Pat is a police officer, what is the probability they will be selected for the committee?

3-2-1kathleen wants to know whether height and shoe size are realted in women. She stops and surveys some female students on the quad and finds the following information:

1)what is the covariance of there data?

2)What is the coefficient of correlation of these data?

3)What is the relationship between the two variables?

a. Can't be determined

b. Weakly positive

c. Strongly positive

d. Moderately negative

Scenario: Imagine you are a researcher who is interested in studying whether sleep deprivation leads to increased reaction times (i.e., being slower) when driving. You randomly select a sample of 30 licensed drivers. Fifteen participants are randomly assigned to get 5 hours of sleep for three consecutive nights. The other 15 participants are randomly assigned to get 8 hours of sleep for three consecutive nights. For the purposes of this Assignment, assume that all participants sleep exactly the required amounts. After the third night, all participants take a driving simulation test that measures their reaction times.

Use SPSS to determine if amount of sleep is related to reaction time.

1. Explain whether the researcher should use an independent-samples t-test or a related-samples t-test for this scenario. Provide a rationale for your decision.
2. Identify the independent variable and dependent variable.
3. Knowing the researcher believes that people who sleep less will have slower reaction times, state the null hypothesis and alternate hypothesis in words (not formulas).
4. Explain whether the researcher should use a one-tailed test or two-tailed test and why.
5. Identify the obtained t value for this data set using SPSS and report it in your answer document.
6. State the degrees of freedom and explain how you calculated it by hand.
7. Identify the p value using SPSS and report it in your answer document.
8. Explain whether the researcher should retain or reject the null hypothesis. Provide a rationale for your decision. Are the results statistically significant?
9. Explain what the researcher can conclude about the relationship between amount of sleep and reaction times.

Data:

Reaction times in seconds for participants with 5 hours of sleep
0.22
0.25
0.27
0.25
0.24
0.28
0.24
0.3
0.25
0.21
0.28
0.23
0.29
0.25
0.29

Reaction times in seconds for participants with 8 hours of sleep
0.21
0.23
0.2
0.24
0.28
0.23
0.3
0.29
0.23
0.21
0.21
0.27
0.29
0.23
0.25

Assume that the distribution of starting salaries for newly qualified CA’s is approximately Normal and has a std deviation of $2,500. We have a random sample of 16 CA’s.

a) Find the probability that the std error (sample std deviation) > $3000.

b) Find the probability that the std error (sample std deviation) < $1500.