A researcher is interested in studying whether a new stretching technique affects the time needed to complete a certain running exercise. The times of 4 randomly selected participants were measured before the new stretching technique was used, and then the times for the same participants were measures after the new technique was used. The resulting data is

Is there a significant difference between the mean times with and without the new stretching technique?

1) What are the appropriate competing hypotheses?

2) What is the value of the test statistics?

3) What are the appropriate degrees of freedom?

4) What id the rejection region

5) p-value

6) test decision

Please Answer the following with as much detail as possible. Thanks!

1. What does a p-value indicate?

2. How does the standard deviation differ from the standard error? (Hint: Don't just describe the difference in the formulas, explain why the formulas are different)

3. How do you know if the results of a sample can be generalized to the entire population?

Police records show the following numbers of daily crime reports for a sample of days during the winter months and a sample of days during the summer months.

Use a 0.05 level of significance to determine whether there is a significant difference between the winter and summer months in terms of the number of crime reports.

State the null and alternative hypotheses.

H₀: The two populations of daily crime reports are not identical.
H_a: The two populations of daily crime reports are identical.H₀: The two populations of daily crime reports are identical.
H_a: The two populations of daily crime reports are not identical.     H₀: Median number of daily crime reports for winter − Median number of daily crime reports for summer < 0
H_a: Median number of daily crime reports for winter − Median number of daily crime reports for summer = 0H₀: Median number of daily crime reports for winter − Median number of daily crime reports for summer ≥ 0
H_a: Median number of daily crime reports for winter − Median number of daily crime reports for summer < 0H₀: Median number of daily crime reports for winter − Median number of daily crime reports for summer ≤ 0
H_a: Median number of daily crime reports for winter − Median number of daily crime reports for summer > 0

Find the value of the test statistic.

W =

Find the p-value. (Round your answer to four decimal places.)

p-value =

What is your conclusion?

Reject H₀. There is not sufficient evidence to conclude that there is a significant difference between the winter and summer months in terms of the number of crime reports.Reject H₀. There is sufficient evidence to conclude that there is a significant difference between the winter and summer months in terms of the number of crime reports.     Do not reject H₀. There is sufficient evidence to conclude that there is a significant difference between the winter and summer months in terms of the number of crime reports.Do not reject H₀. There is not sufficient evidence to conclude that there is a significant difference between the winter and summer months in terms of the number of crime reports.

The stereotypical video game player is a male teenager. However, recent studies suggest that at least 45% of all players are women. A software company has decided to develop and market a sophisticated stock-market video game if the mean age of all video game players is greater than 25. A random sample of video game players will be asked their age to test the relevant hypothesis.

a)In context, explain what the Type I error is.

b)In context, explain what the Type II error is.

c)Which error is worse for the software company, a Type I error or a Type II error? Why?

d)Which error is worse for the video game player, a Type I error or a Type II error? Why?

Suppose that the chance of rain tomorrow depends on previous weather conditions only through whether or not it is raining today and not on past weather conditions. Suppose also that if it rains today, then it will rain tomorrow with probability 0.6, and if it does not rain today, then it will rain tomorrow with probability 0.3, then

a. Calculate the probability that it will rain four days from today given that it is raining today.

b. What is the limiting probability of rain.

What is a effect size that measures the proportion of variance for a one-way between-subjects ANOVA? Which one overestimates the size of an effect in a population?

Thirteen students entered the undergraduate business program at Rollins College 2 years ago. The following table indicates what their grade point average (GPAs) were after being in the program for 2 years and what each student scored on the SAT exam (maximum 2400) when he or she was in high school.

a. Is there a meaningful relationship between grades and SAT scores?

b. If a student scores a 1200 on the SAT, what do you think his or her GPA will be?

c. What about students that score 2400?

Research has shown that 70% of new Small Medium Enterprises (SMEs) are started by graduates while 30% are started by non-graduates. It is also known that 60% of SMEs started by graduates are successful i.e. they survive beyond 3 years, while only 20% of those started by non-graduates are successful.

a) If it is known that a new SME has failed, what is the probability that it was started by a non-graduate? [6]

b) What is the probability that a new SME will be successful? [4

The following data are the monthly salaries y and the grade point averages x for students who obtained a bachelor's degree in business administration. GPA Monthly Salary ($) 2.7 3,600 3.5 3,800 3.6 4,200 3.1 3,700 3.5 4,100 2.8 2,500 The estimated regression equation for these data is ŷ = -55.3 + 1,157.9x and MSE =209,013. a. Develop a point estimate of the starting salary for a student with a GPA of 3.0 (to 1 decimal). $ b. Develop a 95% confidence interval for the mean starting salary for all students with a 3.0 GPA (to 2 decimals). $ ( , ) c. Develop a 95% prediction interval for Ryan Dailey, a student with a GPA of 3.0 (to 2 decimals). $ ( , )

A courier service company has found that their delivery time of parcels to clients is approximately normally distributed with a mean delivery time of 50 minutes and a variance of 25 minutes (squared).

a) What is the probability that a randomly selected parcel will take 60 minutes to deliver? [2]

b) What is the probability that a randomly selected parcel will take between 38.75 and 55 minutes to deliver? [5]

c) What is the probability that a randomly selected parcel will take more than 36.25 minutes to deliver? [3]

d) What is the probability that a randomly selected parcel will take more than 59.25 minutes to deliver? [3]

e) What is the minimum delivery time for the 2.5% of parcels with the longest time to deliver?   

Catalog sales companies mail seasonal catalogs to prior customers. The expected profit from each mailed catalog can be expressed as the product​ below, where p is the probability that the customer places an​ order, D is the dollar amount of the​ order, and S is the percentage profit earned on the total value of an order.

Expected Profit = p X D X S

Typically 12​% of customers who receive a catalog place orders that average ​$180​, and 15​% of that amount is profit.

Complete parts​ (a) and​ (b) below.

​(a) What is the expected profit under these​ conditions? ​$ per mailed catalog

(b) The response rate and amounts are sample estimates. If it costs the company $2.00 to mail each catalog, how accurate does the estimate of p need to be in order to convince you that the expected profit from he next mailing is positive?

the chickens of the ornithes farm are processed when they are 20 weeks old. the distribution of their weights is normal with a mean of 3.8 lb. and a standard deviation of 0.6 lb. On your paper draw a normal curve for each situation and write what you typed in the calculator. Answer the following.

a. What proportion of chickens weigh less than 3 pounds? (Round to 4 decimal places.)

b. What proportion of chickens weigh between 3.5 and 4.5 pounds? (Round to 4 decimal places.)

c. What proportion of chickens weigh more than 5 pounds? (Round to 4 decimal places.)

d. 20 percent of the chickens have a weight below what value? (Round to 1 decimal place.)

e. If I randomly select 5 chickens, what is the probability that they have weights with a mean more than 4 pounds? (Round to 4 decimal places)

A researcher is curious if age makes a difference in whether or not students make use of the gym at a university. He takes a random sample of 30 days and counts the number of upperclassmen (Group 1) and underclassmen (Group 2) that use the gym each day. The data are below. The population standard deviation for underclassmen is known to be 22.57 and the population standard deviation for upperclassmen is known to be 13.57. Upper Classmen average = 202.4, population SD = 13.57, n = 30 Under Classmen average = 191.3, population SD = 22.57, n = 30 Is there evidence to suggest that a difference exists in gym usage based on age? Construct a confidence interval for the data above to decide. Use α=0.10. Confidence Interval (round to 4 decimal places): < μ1 - μ2

Note: For any part below, if it cannot be answered, enter NA.

A quality control company was hired to study the length of meter sticks produced by a certain company. The team carefully measured the length of many many meter sticks, and the distribution seems to be slightly skewed to the right with a mean of 100.03 cm and a standard deviation of 0.13 cm.

a) What is the probability of finding a meter stick with a length of more than 100.12 cm?

b) What is the probability of finding a group of 22 meter sticks with a mean length of less than 100 cm?

c) What is the probability of finding a group of 34 meter sticks with a mean length of more than 100.06 cm?

d) What is the probability of finding a group of 44 meter sticks with a mean length of between 100.02 and 100.05 cm?

e) For a random sample of 50 meter sticks, what mean length would be at the 92nd percentile?

For each of the following problems, define the appropriate parameter(s) and state the null and alternative hypotheses.
1. Is the proportion of men who vote greater than the proportion of women who vote in the United States?
2. A car dealership announces that the mean time for an oil change is less than 15 minutes.
3. A researcher wants to test if there is evidence that the proportion of US citizens who can name the capital city of Canada is greater than 0.75.
4. A researcher wants to see if there is evidence that the mean time spent studying per week is different between first-year students and upper-class students.

My responses so far...?

1. H_a: P_m > P_w - The proportion of men voters is greater than the proportion of female voters in the alternative hypothesis.
H_o: P_m = P_w - The proportion of men voters is equal to the proportion of female votes in the null hypothesis.

2. H_a: Mu < 15 minutes
H_o: Mu = 15 minutes

3. H_a: P_c > 0.75 - The proportion of citizens who can name the capital city of Canada is greater than 0.75 in the alternative hypothesis
H_o: P_c = 0.75 - The proportion of citizens who can name the capital city of Canada is equal to 0.75 in the null hypothesis.

4. I'm really stuck on this one!