An engineer designed a valve that will regulate water pressure on an automobile engine. The engineer designed the valve such that it would produce a mean pressure of 4.0 pounds/square inch. It is believed that the valve performs above the specifications. The valve was tested on 15 engines and the mean pressure was 4.3 pounds/square inch with a standard deviation of 0.7. A level of significance of 0.05 will be used. Assume the population distribution is approximately normal. Determine the decision rule for rejecting the null hypothesis. Round your answer to three decimal places.

Use SPSS for this Application Exercise:
A psychologist hypothesizes that depression increases with aging. It is known that the general population scores a 40 on a standardized depression test where a higher score indicates more depression. The psychologist obtains a sample of individuals that are all over 68 years old. What can the psychologist conclude with α = 0.01? The data are below.

a) What is the appropriate test statistic?
---Select--- na z-test One-Sample t-test Independent-Samples t-test Related-Samples t-test

b)
Population:
---Select--- standardized depression test elderly aging general population depression
Sample:
---Select--- standardized depression test elderly aging general population depression

c) Compute the appropriate test statistic(s) to make a decision about H₀.
(Hint: Make sure to write down the null and alternative hypotheses to help solve the problem.)
p-value =  ; Decision:  ---Select--- Reject H0 Fail to reject H0

d) Using the SPSS results, compute the corresponding effect size(s) and indicate magnitude(s).
If not appropriate, input and/or select "na" below.
d =  ;   ---Select--- na trivial effect small effect medium effect large effect
r² =  ;   ---Select--- na trivial effect small effect medium effect large effect

e) Make an interpretation based on the results.

The elderly are significantly more depressed than the population.

The elderly are significantly less depressed than the population.    

The elderly did not significantly differ on depression than the population.

A researcher was interested in the effects of caffeine on sleep. She measured how many minutes it took for ten participants to fall asleep. Half of the participants drank a liter of caffeinated soda before going to sleep while the other half were only allowed to drink water. Summary data of minutes are presented below. Did the caffeine increase the length of time it took to fall asleep (a =.05)? (27 points total for 6a-e)

         Water Group Caffeine Group

                     18 22

                     15 15

                     19 20

                     14 21

                     14 19

a. Name the test to be conducted and why you selected it:

b. State the null and alternative hypotheses:

c. State the CV and the decision rule. Sketch the rejection region:

d. In SPSS, calculate the observed test statistic. Paste your answer here or attach it to your assignment. In addition, calculate the value of eta2 (h2).

e. Write out an APA style conclusion based on this finding:

Using Grocery Rewards ~ A Gallup Poll of 500 randomly selected American adults resulted in 405 stating they use a grocery stores’ rewards card to save money on their grocery purchases. A local grocery store manager comes to you for help to use these results to provide an estimate of the population proportion of all American adults who use a grocery stores’ rewards card to save money on their grocery purchases. You ask the manager what confidence level should be used ~ 90%, 95%, 98% or 99%. The manager says “I am not sure what the confidence level really means, but use 98% I guess”.

You create the following list to help you remember the various items you need to include in your response back to the manager:

Assumptions: You know you may assume a random sample of 500 American adults was selected. You plan to both state and check the remaining necessary assumption.
Computations: You will compute and report the 98% confidence interval, showing all work so the manager can follow your computations.
Level Explanation: Since the manager was unclear what the confidence level means, you will include a sentence to explain it, that is, provide an interpretation of the 98% confidence level in context.

When conducting a statistical hypothesis test, a very small p value indicates strong evidence against the null hypothesis. Why?

A union leader in the Maritime Workers' Union believed that workers at the Port of Brisbane were receiving a lower weekly salary than workers at Port Kembla. To determine whether this claim was valid, they took samples of size 17 and 11 in Brisbane and Port Kembla, respectively, and found that the average and standard deviation of the weekly salaries were $914.11 and $49.38 respectively in Port Kembla, and $859.23 and $55.62 in Brisbane. Use Brisbane minus Port Kembla, and answer correct to two decimal places. 1. Determine a point estimate for the difference in the average weekly salary between the two ports. ? 2. Calculate the standard error for the difference between sample means assuming that the workers' salaries in both locations are normally distributed and have the same population variance. ? 3. Use Kaddstat to determine a 95% confidence interval for the difference between the mean weekly salaries in Brisbane and Port Kembla. lower limit ? upper limit ?

In a large city’s recent mayoral election, 131,506 out of 309,153 registered voters actually turned out to vote. If 20 registered voters are randomly selected, find the probability that 7 of them voted in the mayoral election. Use a TI-83, TI-83 plus, or TI-84 calculator to find the probability.

A company would like to determine the relationship between: the time (in years) spent at the company and the employee’s hourly pay. The data for 5 employees are listed in the table below. Calculate and interpret the correlation coefficient r. Include a plot of the data in your discussion.

a. Calculate the Pearson correlation coefficient for the data.

b. Use an appropriate 2-tailed hypothesis test (ɑ = .05) to determine whether this relationship is statistically significant.

c. Based on your calculations, what can we conclude about the relationship between the time spent at the company and hourly pay?

1. Nutrient loss in food products is an important issue for food processing companies. We

would like to determine whether or not bread loses its vitamin C content over time.

a. Go to the Excel spreadsheet “Vitamin C in bread” that is posted with this assignment and

download it. There you will find results of an experiment conducted by a baking company.

The data show vitamin C content of 20 loaves of bread. Five of the loaves had vitamin C

measured the day of baking (day 0). Another five had vitamin C measured one day after

baking (day 1), and so forth for days 3 and 5.

b. Click Tools > Data Analysis and select the appropriate procedure for doing an analysis of

variance. I want to see a printout of the results obtained by using the Data Analysis Tool.

c. Interpret the results. Are there differences among the days in terms of vitamin C content?

What in the output tells you this?

2. Go the Excel spreadsheet “Trends in Vitamin C in bread” that is posted with this

assignment. There you will find the same data as in problem 1 but in a format that will allow

you to get a scatterplot and trendline.

a. Obtain the scatterplot and trendline (include the equation). I want to see a printout of this

analysis.

b. Use the equation in 2a to predict vitamin C content when day = 2. Include the answer on

your spreadsheet.

A random sample of n = 64 observations has a mean x = 29. 1, and a standard deviation of s = 3.9. Find a 90 % confidence interval for the population mean.. A major department store chain is interested in estimating the average amount its credit card customers spent on their first visit to the chain's new store in the mall. Fifteen credit card accounts were randomly sampled and analyzed with the following results: = $50.50 and = 400. Find a 95% confidence interval for the average amount the credit card customers spent on their first visit to the chain's new store in the mall.

Is there enough evidence in the data that population average price of diamond for color “E” is more than 1500?

Solve in R using the t test.

Assume the age of death for all us burials(of persons over 5 years old) is approximately normally distributed and the sample mean is 68.84 and the standard deviation is 18.402926789.

Find the age at death such that 1.5% of US burials (of persons over 5 years old) were at least that old.

Find the probability that a burial randomly selected from all US burials (of persons over 5 years old) involved a person at least 30 years old.

Find the probability that a burial randomly selected from all US burials ( of persons over 5 years old) involved a person at most 85 years old.

Which of the following are true about all normal distributions? Check all that apply
A. They are symmetric.
B. They are all centered at zero.
C. They have one large tail.
D. They are categorically sharp.

I chose A and D but I still get errors . I dont know if my answer wrong or I have to add one more

Probability Plot Problem:

Considering the following observations for X:

X = [19.0, 16.0, 14.0, 13.0, 12.0, 11.0, 10.5, 10, 9.7, 9.2, 8.7, 8.5]

a) Use Minitab to determine the type of probability distribution for X. Cut & paste the chart and briefly describe the reason for your answer.

b) Use the trendline in Excel to determine the equation f(x) for the observations. Cut & paste the chart with the trendline equation.

c) According to the above f(x), what is the predicted value of the next observation in the series?

_____________________________________________

Assume that 15​% of people are​ left-handed. If 6people are selected at​ random, find the probability of each outcome described below.

​a) Find the probability that the first lefty is the sixth person chosen.

​(Round to four decimal places as​ needed.)

​b) Find the probability that there are some lefties among the 6 people.

​(Round to four decimal places as​ needed.)

​c) Find the probability that the first lefty is the fourth or fifth person.

​(Round to four decimal places as​ needed.)

​d) Find the probability that there are exactly 2 lefties in the group.

​(Round to four decimal places as​ needed.)

​e) Find the probability that there are at least 4 lefties in the group.

​(Round to four decimal places as​ needed.)

​f) Find the probability that there are no more than 2 lefties in the group.

​(Round to four decimal places as​ needed.)