A watch manufacturer believes that 60% of men over age 50 wear watches. So, the manufacturer took a simple random sample of 275 men over age 50 and 170 of those men wore watches. Test the watch manufacturer's claim at α = .05.

Currently, among the 20 individuals of a population, 2 have a certain infection that spreads as follows: Contacts between two members of the population occur in accordance with a Poisson process having rate ?. When a contact occurs, it is equally likely to involve any of the possible pairs of individuals in the population. If a contact involves an infected and a non-infected individual, then, with probability p the non-infected individual becomes infected. Once infected, an individual remains infected throughout. Let ?(?) denote the number of infected members of the population at time t. Considering the current time as t = 0, we want to model this process as a continuous-time Markov chain.

(a) What is the state space of this process?

(b) What is the probability that an infected person contacts a non-infected person?

(c) What is the rate at which an infected person contacts a non-infected person (we denoted this type of contact by I-N contact) when there are X infected people in the population?

(d) Is the inter-contact time between two I-N contacts exponentially distributed? Why?

(e) Compute the expected time until all members of the considered population are infected.

Scenario

Certified Behavior Analysts claim that their procedures are more effective than any other.  Their procedures are clear-cut analytics that anyone can learn and apply. It’s not an art they proclaim, but a science.  You decide to put it to test.  You interview and survey the parents of autistic kids, loved ones of the depressed, and former sufferers of phobias, who had been treated with Behavior Therapy, Drug Therapy, and Play Therapy.  Your survey generates a score from 1-100 with higher values indicating greater effectiveness of the therapy and 85 and above indicates complete resolution of the problem.  

            Behavior Therapy                   Drug Therapy              Play Therapy

            58, 65, 71, 59,                         59, 68, 32, 44              58, 61, 50, 60

            81, 74, 83, 63                          38, 41, 30, 51              64, 62, 85, 57

Instructions:

1. Using the above data calculate the one-way analysis of variance in JASP. Report the F-ratio in APA style, including the p-value and eta-squared (treatment magnitude).

10 points

2. If the one-way ANOVA shows a significant difference among the groups, then calculate post hoc test to determine which groups are different – be sure you compare each group to each other group. Report the significant differences among the groups. If the one-way ANOVA does not show a significant difference, then state no difference.  

15 points

3. Calculate the mean and standard deviations for all three groups and report in an APA table. You may use the one generated by JASP.

10 points

4. Write a short APA summary of your conclusions. Make sure to use the data to support conclusions.

*Please use JASP*

It is estimated that 4.5% of the general population will live past their 90th birthday. Suppose a random sample of 753 high school seniors is selected.

a. Describe the sampling distribution of ?̂.

b. What is the probability that from this random sample taken, the sample proportion of these high school seniors who will live past their 90th birthday is between 0.043 and 0.056?

A company randomly chose 200 US households and found that in 120 of them, the women made the majority of the purchasing decisions. We want to know the population proportion of US housholds where women make the majority of purchasing decisions. Construct a 96% confidence interval to find p.  

a) what is p hat?

b) what is alpha?

c) what is the value of the test statistic

d) what is the value of the standard errror

e) what is the value of the margin of error

f) what is the lower boundary of the confidence interval

g) what is the upper boundary of the confidence interval

#40

The quantity of dissolved oxygen is a measure of water pollution in lakes, rivers, and streams. Water samples were taken at four different locations in a river in an effort to determine if water pollution varied from location to location. Location I was 500 meters above an industrial plant water discharge point and near the shore. Location II was 200 meters above the discharge point and in midstream. Location III was 50 meters downstream from the discharge point and near the shore. Location IV was 200 meters downstream from the discharge point and in midstream. The following table shows the results. Lower dissolved oxygen readings mean more pollution. Because of the difficulty in getting midstream samples, ecology students collecting the data had fewer of these samples. Use a 5% level of significance. Do we reject or not reject the claim that the quantity of dissolved oxygen does not vary from one location to another?

(b) Find SS_TOT, SS_BET, and SS_W and check that SS_TOT = SS_BET + SS_W. (Use 3 decimal places.)

Find d.f._BET, d.f._W, MS_BET, and MS_W. (Use 3 decimal places for MS_BET, and MS_W.)

Find the value of the sample F statistic. (Use 3 decimal places.)


What are the degrees of freedom?
(numerator)
(denominator)

(f) Make a summary table for your ANOVA test.

The National Sleep Foundation surveyed representative samples of adults in six different countries to ask questions about sleeping habits.† Each person in a representative sample of 250 adults in each of these countries was asked how much sleep they get on a typical work night. For the United States, the sample mean was 391 minutes, and for Mexico, the sample mean was 426 minutes.

The report also gave data for representative samples of 250 adults in Canada and in England. The sample mean amount of sleep on a work night was 423 minutes for Canada and 409 minutes for England. Suppose that the sample standard deviations were 35 minutes for the Canada sample and 41 minutes for the England sample.

(a)

Construct a 95% confidence interval estimate of the difference in the mean amount of sleep (in minutes) on a work night for adults in Canada and adults in England. (Use

μ_Canada − μ_England.

Round your answers to three decimal places.)

,

minutes

Interpret the interval.

We are 95% confident that the difference in the mean amount of sleep on a work night for the adults studied in Canada and England falls within this interval.There is a 95% chance that the difference in the mean amount of sleep on a work night for adults in Canada and adults in England falls directly in the middle of this interval.    There is a 95% chance that the true difference in the mean amount of sleep on a work night for adults in Canada and adults in England falls directly in the middle of this interval.There is a 95% chance that the difference in the mean amount of sleep on a work night for adults in Canada and adults in England falls within this interval.We are 95% confident that the true difference in the mean amount of sleep on a work night for adults in Canada and adults in England falls within this interval.

(b)

Based on the confidence interval from part (a), would you conclude that there is evidence of a difference in the mean amount of sleep on a work night for the two countries? Explain why or why not.

The confidence interval  ---Select--- (does not allow us/allows us to) conclude that there is evidence of a difference in the mean amount of sleep on a work night for the two countries because zero  ---Select--- (is not,is) contained in the confidence interval.

We wish to estimate what percent of adult residents in a certain county are parents. Out of 100 adult residents sampled, 74 had kids. Based on this, construct a 99% confidence interval for the proportion p of adult residents who are parents in this county.

Express your answer in tri-inequality form. Give your answers as decimals, to three places.

< p <  Express the same answer using the point estimate and margin of error. Give your answers as decimals, to three places.

Class data (hours on electronics) are below.. please use data fto answer question...

1. A national survey conducted by Common Sense Media in early 2017 found that the average amount of time in front of various electronic devices was 6 hours and 40 minutes. I believe that this actual number of hours is less than this. Using our class data, at α=.05 is there enough evidence to support my claim?

Hours on electronics 6,6.5,4,1,8,8,0.5,4,4,9,4,3,3,2,4,4,3,3,2,2,3,4,1,6,3,5,8,3,2,4,6,4,4,5,6,4,1,1,13,0.75,10,2,9,6,9,6,5,2,3.5,8,4,3,4,2,1.5,6,4,2,3,6,10,8,4,2,4,3,4,7,6,8,4.5,5,2,7,12,3,4.5,11,8,6,5,8,7,8,2,6,2,7,5,4,2,2,1,3,4,4,2,2,1,6,4,6,7,9,5,2,7,11,10,3,10,2.5,4.5,5,5,4,8,9,2,14,12,6,18,6,14,12,8,10,15,16,16,15,16,10,15,17,8,17,17,5,3,2,3,4,5,3,4,2,4,6,6,4,9,5,10,5,9,2,8,12,5,1,5,6,8,5,10,8,10,6,5,10,2,3,10,2,3.5,2.5,2,5,4,0,4,2,2,6,7,1,3.

A survey of mining companies is to be conducted to estimate p, the proportion of companies that anticipate hiring engineers during the coming year. (a) How large a sample is required to estimate p to within 0.04 with 95% confidence? (b) A sample of 500 yields 105 companies that plan to hire such engineers. Give the 95% confidence interval for p.

Currently students have several popular fast food options (e.g. Chick fil A, Wendy’s, Papa Johns, Au Bon Pain), cafeterias (Muse, Dalton), and take out (Hisso Sushi, Pinkberry).  Currently Chartwell Food Services is the licensed operator for all food options on campus.  The company has developed a short 10-minute survey to complete in whatever manner would produce the best results.     Research questions involve the most preferred food vendors, most preferred food types, preferred locations, and price points.  Develop a sampling plan that would yield generalizable results regarding the lunch and dinner habits of Radford University students.  Explain your choices.

A process has a Cpk = 1.35 and is centered between the specification limits. (a) What is the DPM of the process? (b) If the mean of the process increases by 1.5σ the DPM would be?

5.

California and Washington state both started reporting COVID-19 cases at approximately the same time. Suppose a researcher wants to study the fatality rate of diagnosed COVID-19 cases in the 2 states.

a. What null hypothesis should be used? Pick one and explain.

i. California has a higher fatality rate than Washington.
ii. California has lower higher fatality rate than Washington.
iii. California has a different fatality (possibly higher, possibly lower) rate than Washington. iv. California and Washington have the same fatality rate.

b. What alternate hypothesis should be used? Pick one and explain.

i. California has a higher fatality rate than Washington.
ii. California has lower higher fatality rate than Washington.
iii. California has a different fatality (possibly higher, possibly lower) rate than Washington. iv. California and Washington have the same fatality rate.

c. As of 3/24/2020, California had 2220 cases and 100 fatalities, compared to 111 fatalities in 2221 cases in Washington. Use your calculator to carry out a suitable hypothesis test. Report the p-value of the test, determine whether or not to reject the null, and state what should be concluded. Use ? = .05.

Career Training According to the study The American Freshman: National Norms 2015, 76.1% of college freshmen said that “to get training for a specific career” was a very important reason for their going to college. Consider a group of seven freshman selected at random. In Exercises 23–26, find the probabilities that the number of people in the group who felt that the reason was very important is as stated. 23. All seven 24. Exactly three of the seven 25. At least six of the seven 26. No more than two of the seven