A manufacturing company produces electrical insulators. If the insulators break when in use, a short circuit is likely to occur. To test the strength of the insulators, destructive testing is carried out to determine how much force is required to break the insulators. Force is measured by observing the number of pounds of force applied to the insulator before it breaks. The data shown below are from 30 insulators subjected to this testing:

1. At the 0.05 level of significance, is there evidence that the population mean force required to break the insulator is greater than 1,500 pounds?
2. What assumption about the population distribution is needed in order to conduct the t test in (a)?
3. Construct a histogram or a boxplot, or a normal probability plot to evaluate the assumption made in (b).
4. Do you think that the assumption needed in order to conduct the t test in (a) is valid? Explain.

The Tinyton Public School Board is taking bids on the city’s four school bus routes. Four companies have made bids. X denotes that a particular company did not make a bid on a particular route.

1. Assume the bidder can be assigned only one route. Minimize Tinyton’s cost of running the four bus routes. (10 points)
2. Assume the bidder can be assigned two routes. Minimize Tinyton’s cost of running the four bus routes. (10 points)

Question 8: A machine at AMT & Co. fills 120-ounce jugs with laundry softener.
A quality control inspector wishes to test if the machine underfills the jugs or not. Assume
the distribution of the amount of laundry softener in these jugs is Normal. Under “standard”
circumstances, the mean amount should be 120 ounces with a standard deviation of 1 ounce.
a. (2 mark) What are the hypotheses the quality control inspector wishes to test?
b. Suppose the quality control inspector wishes to conduct the test using α = 0.10
and a sample size of 40. What is the range of values of ̄x for which he will accept H0?
c. Suppose the quality control inspector wishes to conduct the test using α = 0.10
and a sample size of 40. If the true mean amount of detergent in these jugs is 119.5 ounces,
what is the power of the test?
d. If the observed sample mean amount in the simple random sample of 40 jugs
equals 119.62 ounces, find the P-value.

Match each situation with the correct statistical technique.

Group of answer choices:

1. Histogram
2. Wilcoxon Rank Sum           
3. Chi-square test           
4. Two sample t test            
5. Median (Q1, Q3)           
6. Count (%)           
7. Bar Graph           
8. ANOVA            
9. Kruskal Wallis Test           
10. Fisher's Exact Test       

1. Outcome is continuous, predictor has two categories. Only have 20 observations.
2. Descriptive Statistics for a Categorical Variable
3. Both variables are categorical. Only have 20 observations.
4. Outcome is continuous, predictor has two categories. Have 500 observations.
5. Descriptive Statistics for a Continuous Variable
6. Outcome is continuous, predictor is categorical (3 or more categories). Variance in each category is relatively similar.
7. Both variables are categorical. Have 1000 observations.
8. Outcome is continuous, predictor is categorical (3 or more categories). Variance in each category is vastly different.
9. Visual display for a continuous variable     
10. Visual display for a categorical variable

A psychologist conducted a survey of the attitude towards the sustainability of American energy consumption with 250250 randomly selected individuals several years ago. The psychologist believes that these attitudes have changed over time. To test this he randomly selects 250250 individuals and asks them the same questions. Can the psychologist confirm his theory that the attitudes have changed from the first survey to the second survey?

Copy Data

Step 1 of 10:

State the null and alternative hypothesis.

Step 2 of 10:

What does the null hypothesis indicate about the proportions of respondents with each attitude?

Step 4 of 10:

Find the expected value for the number of respondents who are optimistic. Round your answer to two decimal places. E(n optimistic) =

Step 5 of 10:

Find the expected value for the number of respondents who are pessimistic. Round your answer to two decimal places. E(n Pessimistic) =

Step 6 of 10:

Find the value of the test statistic. Round your answer to three decimal places.

Step 7 of 10:

Find the degrees of freedom associated with the test statistic for this problem.

Step 8 of 10:

Find the critical value of the test at the 0.05 level of significance. Round your answer to three decimal places.

Step 9 of 10:

Make the decision to reject or fail to reject the null hypothesis at the 0.05 level of significance.

Step 10 of 10:

State the conclusion of the hypothesis test at the 0.05 level of significance.

A queueing system serves two types of customers. Type 1 customers arrive according to a Poisson process with a mean rate of 5 per hour. Type 2 customers arrive according to a Poisson process at a mean rate of 3 per hour. The system has two servers, both of which serve both types of customer. All service times have exponential distribution with a mean of 10 minutes. Service is provided on a first-come-first-served basis.

a. What is the probability distribution of the time between consecutive arrivals of customers of any type, what is its mean?

b. Assume that when a Type 2 customer arrives, he finds two Type 1 customers being served and no other customers in the system. What is the probability distribution of this Type 2 customer’s waiting time in the queue and its mean?

A poll was conducted on voter’s opinions on two candidates with margin of errors at 3.5%. Candidate A 38% Candidate Z 41% Undecided 21%

(a) Can we conclude that Candidate Z has a clear statistical lead over Candidate A? Briefly justify your answer.

(b)  Assuming 95% of confidence level, estimate the number of people participated in the poll. Round your answer to the nearest whole number.

A study is done to test the claim that Company A retains its workers longer than Company B. Company A samples 16 workers, and their average time with the company is 5.2 years with a standard deviation of 1.1. Company B samples 21 workers, and their average time with the company is 4.6 years with a standard deviation of 0.9. The populations are normally distributed

In a study of red/green color blindness, 1000 men and 700 women are randomly selected and tested. Among the men, 92 have red/green color blindness. Among the women, 19 have red/green color blindness. Test the claim that men have a higher rate of red/green color blindness.
The test statistic is
The p-value is

1. In the iris data, build a linear regression model to predict Sepal.Length based on both Petal.Length and Species.

a. Calculate the regression equation, including the interaction.

b. From this equation, you should be able to find 3 regression lines (one for each Species). Interpret each of the 3 slopes of the lines in the context of the problem. Remember that both numerical variables are measured in centimeters.

c. Plot the 3 regression lines in a scatterplot of Sepal.Length vs. Petal.Length. Use a different color for each Species.

d. Predict the Sepal.Length for a Versicolor iris with a petal that is 3.4 cm long.

e. Conduct a partial ?-test to see if the Petal.Length:Species interaction terms are significant. State the hypothesis, ?-value, and conclusion of the test.

f. Now calculate the regression equation without the interaction term. Interpret the slope in the context of the problem.

g. Using the no-interaction model, I’m 90% sure that the sepal length of a Virginica iris with a 5.5-cm-long petal will be between __________ cm and __________ cm.

h. Identify and interpret the ? 2 from the no-interaction model.

Using the naïve method (most recent value) as the forecast for the next year, what are the following measures of forecast accuracy

1) Mean absolute error

2) Mean squared error

3) Mean absolute percentage error

4) What is the forecast for year 11?

Consider the data below:

Options

• A. 1) 72.44     2) 8263.11     3) 18.86%     4) 436
• B. 1) 72.44     2) 8263.11     3) 34.45%     4) 586
• C. 1) 81.67      2) 4592.51     3) 18.86%     4) 436
• D. 1) 72.44      2) 8263.11   3) 18.86%     4) 785

The effect of phosphate supplementation on bone formation was assessed in six healthy adult dogs. For each dog, bone formation was measured for a 12-week period of phosphate supplementation as well as for a 12-week control period. Here are the results in percent growth per year:

The authors concluded that phosphate supplementation significantly increased bone formation compared to the control. Do an analysis to verify this statement.

A) State the null and alternative hypotheses.

B) What is the P –value for this test?

C) What is your conclusion? Reject H₀ or Do not reject H₀?

D) Write a sentence describing your conclusion.

The following sample data reflect shipments received by a large firm from three different vendors and the quality of those shipments. (You may find it useful to reference the appropriate table: chi-square table or F table) Vendor Defective Acceptable 1 28 126 2 12 78 3 33 246 a. Select the competing hypotheses to determine whether quality is associated with the source of the shipments. H0: Quality and source of shipment (vendor) are independent.; HA: Quality and source of shipment (vendor) are dependent. H0: Quality and source of shipment (vendor) are dependent.; HA: Quality and source of shipment (vendor) are independent. b-1. Calculate the value of the test statistic

1. Data were collected on number of credit hours earned from a random sample of 40 JMU students. The mean was 57.2 and the standard deviation was 8.9. Conduct a test to determine whether the true mean number of credit hours earned differs from 55.0, allowing a Type I error rate of 0.05. Assume that the distribution of the number of credit hours earned is normal. Show your full work. You may not use your calculator’s built-in function.