-Formulate both null and alternative hypotheses for the client, and explain why the hypotheses need to be directional or non-directional.

-Determine what statistical test should be used to analyze the data.

-Summarize all information used to determine the correct statistical test (e.g., number of groups, type of data collected, independent or repeated measures)

-Provide a sample size and critical values in relation to the hypothesis.

-State what statistical test should be used (be specific since you have all of the information you need to determine the critical value(s)).

-Discuss what the statistical analysis will do in answering the hypotheses and question(s) for the client. Also discuss any potential problems to watch out for, including an appropriate sample size to meet the assumptions of the statistical test.

Client Scenario: Jackson Hole Mind and Body Works

My name is Jane, and I am a licensed counselor who owns a business in Jackson Hole, Wyoming. This past year, I started a couple laughing yoga classes that combine the anxiety removing benefits of yoga with the emotional release of laughter. It has been a lot of fun and many clients love it, but a competitor has been criticizing my new approach as a sham and quackery. I am confident that my laughing yoga classes are beneficial, but I would like you to perform a study that examines the impact of my approaches from a scientific perspective. I know that science needs to be objective, so I would like you to setup a study for me as a nonbiased researcher. My thoughts are that I could give you the email addresses of clients who are willing to be in the study, and you would ask each of them questions, and then analyze the results.

            I would like you to examine two types of therapy I conduct, my laughing yoga therapy and my more traditional cognitive behavioral therapy.   I expect that 40 participants will be available from my laughing yoga classes, and that 50 participants will be available from my traditional cognitive behavioral therapy sessions. It would be nice if you asked questions related to clients’ current healthy living practices and use of positive emotions. You can determine the exact questions to ask clients. I was thinking that I would offer each participant in the study a couple free smoothie drinks at a local juice bar for participating in the research.

Write an R function max.streak(p) that gives the length of the maximum "streak" of either all heads or all tails in 100 flips of a (possibly biased) coin whose probabilty of showing heads is pp.

Use your function to determine the expected length (rounded to the nearest integer) of the maximum streak seen in 100 flips of a coin when the probability of seeing "heads" is 0.700.70.

As a check of your work, note that the expected length of the maximum streak seen in 100 flips of a fair coin should be very close to 7.

a. An experiment was performed on a certain metal to determine if the strength is a function of heating time (hours). Results based on 25 metal sheets are given below. Use the simple linear regression model.
∑X = 50
∑X² = 200
∑Y = 75
∑Y² = 1600
∑XY = 400

Find the estimated y intercept and slope. Write the equation of the least squares regression line and explain the coefficients. Estimate Y when X is equal to 4 hours. Also determine the standard error, the Mean Square Error, the coefficient of determination and the coefficient of correlation. Check the relation between correlation coefficient and Coefficient of Determination. Test the significance of the slope.

b. Consumer Reports provided extensive testing and ratings for more than 100 HDTVs. An overall score, based primarily on picture quality, was developed for each model. In general, a higher overall score indicates better performance. The following (hypothetical) data show the price and overall score for the ten 42-inch plasma televisions (Consumer Report data slightly changed here):

Use the above data to develop and estimated regression equation. Compute Coefficient of Determination and correlation coefficient and show their relation. Interpret the explanatory power of the model. Estimate the overall score for a 42-inch plasma television with a price of $3600 and perform significance test for the slope.

(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.)

The population of Nevada, P(t), in millions of people, is a function of t, the number of years since 2010. Explain the meaning of the statement P(8) = 3. Use units and everyday language. (1 point)
2. Find the slope-intercept form of the equation of the line through the points (8, 25) and (-2, -13). (2 points)
3. At 8am, Charles leaves his house in Spartanburg, SC and drives at an average speed of 65 miles per hour toward Orlando, FL. At 11:45am, he stops for lunch in Savannah, GA, which is 276.25 miles from Orlando. a. Find a linear formula that represents Charles’ distance, D, in miles from Orlando as a function of t, time in hours since 8am. (2 points)
b. Find and interpret the horizontal intercept. Remember to write your intercept as a point! (2 points)
c. Find and interpret the vertical intercept. Remember to write your intercept as a point! (2 points)
1
2
4. The temperature in ◦F of freshly prepared soup is given by T(t) = 72 + 118e−0.018t, where t represents time in minutes since 6pm when the soup was removed from the stove. a. Determine the value of T(30) and interpret your answer in everyday language. (2 points)
b. Find and interpret the vertical intercept. Remember to write your intercept as a point! (2 points)
5. Decide whether the following function is linear. Explain how you know without finding the equation of the line.
x 9 12 16 23 34 f(x) 26.6 36.2 49 74.9 110.1
6. Attendance at a local fair can be modeled by A(t) = −30t2 + 309t + 20 people, where t represents the number of hours since 10am. a. Find the average rate of change of the attendance from t = 3 to t = 8. Give units. (2 points)
b. Interpret your answer from (a) in everyday language.

NO HANDWRITTEN ANSWERS PLEASE

The most common abuse of correlation in studies is to confuse the concepts of correlation with those of causation.

Good SAT scores do not cause good college grades, for example. Rather, there are other variables, such as good study habits and motivation, that contribute to both. Find an example of an article that confuses correlation and causation.

Discuss other variables that could contribute to the relationship between the variables.

Bass - Samples: The bass in Clear Lake have weights that are normally distributed with a mean of 1.9 pounds and a standard deviation of 0.8 pounds.

(a) If you catch 3 random bass from Clear Lake, find the probability that the mean weight is less than 1.0 pound. Round your answer to 4 decimal places.


(b) If you catch 3 random bass from Clear Lake, find the probability that the mean weight it is more than 3 pounds. Round your answer to 4 decimal places.

Why are sampling distributions important to the study of inferential statistics? In your answer, demonstrate your understanding by providing an example of a sampling distribution from an area such as business, sports, medicine, social science, or another area with which you are familiar. Remember to cite your resources and use your own words in your explanation.

1) A manufacturer of cereal claims that the mean weight of a particular type of box of cereal is 1.2 pounds. A random sample of 71 boxes reveals a sample average of 1.186 pounds and a sample standard deviation of .117 pound. Using the .01 level of significance, is there evidence that the average weight of the boxes is different from 1.2 pounds?

Is the test statistic for this test Z or t?

Select one:

a. t

b. z

2) A manufacturer of cereal claims that the mean weight of a particular type of box of cereal is 1.2 pounds. A random sample of 71 boxes reveals a sample average of 1.186 pounds and a sample standard deviation of .117 pound. Using the .01 level of significance, is there evidence that the average weight of the boxes is different from 1.2 pounds?

What is the value of the test statistic of the test? ( Enter 0 if this value cannot be determined with the given information.)

3) A manufacturer of cereal claims that the mean weight of a particular type of box of cereal is 1.2 pounds. A random sample of 71 boxes reveals a sample average of 1.186 pounds and a sample standard deviation of .117 pound. Using the .01 level of significance, is there evidence that the average weight of the boxes is different from 1.2 pounds?

What is the pvalue of the test? (Enter 0 if this value cannot be determined with the given information.)

4) A manufacturer of cereal claims that the mean weight of a particular type of box of cereal is 1.2 pounds. A random sample of 71 boxes reveals a sample average of 1.186 pounds and a sample standard deviation of .117 pound. Using the .01 level of significance, is there evidence that the average weight of the boxes is different from 1.2 pounds?

What is the relevant bound of the rejection region? (Enter 0 if this value cannot be determined with the given information.)

5) A manufacturer of cereal claims that the mean weight of a particular type of box of cereal is 1.2 pounds. A random sample of 71 boxes reveals a sample average of 1.186 pounds and a sample standard deviation of .117 pound. Using the .01 level of significance, is there evidence that the average weight of the boxes is different from 1.2 pounds?

What decision should be made?

Select one:

a. Do not reject the null hypothesis

b. Can not be determined from given information

c. Accept the null hypothesis

d. Reject the null hypothesis

Norrie sees two lights flash at the same time, then one of them flashes every 4th second, and the other flashes every 5th second. How many times do they flash together during a whole minute?

Twocombinationdrugtherapies(TreatmentAandTreatmentB)have been developed for eradicating Helicobacter pylori in human patients. The effectiveness of these treatments depends on whether or not the patient is resistant to the chemical compound Metronidazole, but apatient’s resistance status is not routinely determined before beginningtreatment. Treatment A successfully eradicates Helicobacter pylori in 92% of resistant patients and 87% of non-resistant patients. The corresponding proportions for Treatment B are 75% and 95%.

(i) Denote by θ (0 < θ < 1) the proportion of the affected population that is resistant. If a patient from this population is unsuccessfully treated with Treatment B, write down an expression for the probability that the patient is resistant.

(ii) For what values of θ would a greater proportion of patients from this population be successfully treated by Treatment B than by Treatment A?

(iii) Suppose that θ = 0.2. If 20 patients, selected at random from the affected population, are independently treated with Treatment B, find the probability that at least 18 of them will be treated successfully.

A survey conducted of 1,000 college students asked those who regularly drink alcohol, how many alcoholic beverages they consume each week. From this survey, on average (mean), these students consume five beverages each week. These data are normally distributed. The mean, median and mode are equal, and the standard deviation is 1.

1. How many of these students consume five or more alcoholic beverages each week?

2. What is the probability that a student in this study will consume five or more alcoholic beverages each week? (decimal)

3. How many of these adolescents consume five or less alcoholic beverages each week?

4. What is the probability that a student in this study will consume five or less alcoholic beverages each week? (decimal)

5. How many of these adolescents consume between four and six alcoholic beverages each week? 6. What is the probability that a student in this study will consume from four to six alcoholic beverages each week? (decimal)

Given their performance record and based on empirical rule what would be the lower bound of the range of sales values that contains 68% of the monthly sales?

The probability of winning in a certain state lottery is said to be about 1/9. If it is exactly 1/9, what a random variable represents the distribution of the number of tickets a person must purchase up to and including the first winning ticket? Plot the PMF of this random variable. the distribution of the number of tickets purchased up to and including the second winning ticket can be described by what distribution?