Assume that the heights of men are normally distributed with a mean of 69.0 inches and a standard deviation of 2.8 inches. If 1 man is randomly selected, find the probability that he has a height between 68 and 70 inches.

Let X denote the time in minutes (rounded to the nearest ½ minute) for blood samples to be taken from patients in UrgentCare clinic near Mountainside, NJ. A random survey of 200 patients revealed the following frequency distribution in minutes.
X = x (mins)
0 0.5 1.0 1.5 2.0 2.5
Freq (# of patients)
20 38 62 44 14 22
Determine the following:
a) P (X < 2.0)
b) P (0.75 < X ≤ 1.5)
c) P (X ≥ 2.0)
d) P (X = 1.5)
e) Mean and standard deviation of the random variable X
f) Interpretation of mean of random variable X.
g) Draw a probability histogram (pdf) for the random variable X and locate the mean (draw a vertical dash line to indicate the mean) in a graph. Mark the x-axis and y-axis and indicate the variables and the scales appropriately.
h) Construct the c.d.f. for the random variable X in a graph formats. Mark the x-axis and y-axis and indicate the variable and the scale appropriately.

The credit department of Lion’s Department Store in Anaheim, California, reported that 26% of their sales are cash, 27% are paid with a credit card, and 47% with a debit card. Twenty percent of the cash purchases, 86% of the credit card purchases, and 61% of the debit card purchases are for more than $50. Ms. Tina Stevens just purchased a new dress that cost $120. What is the probability that she paid cash? (Round your answer to 3 decimal places.)

A) Probability:

Nike claims that the number of miles a jogger can get a on a pair of Nike’s running shoes is higher than 1000. Moreover, Nike also claims that their shoes outperform Adidas shoes by more than 15 miles. We have samples of 150 joggers using Nike shoes and 170 using Adidas shoes. The sample average of miles they got are 1015 for Nike and 995 for Adidas. The sample standard deviations are 100 for Nike and 50 for Adidas.

a.) At a 5% level of significance, is there statistical evidence showing that Nike shoes get more than 1000 miles?

b.) Obtain the p-value for the previous test. What does it mean?

c.) At a 5% level of significance, is there statistical evidence showing that Nike shoes outperform Adidas shoes?

d.) Obtain the p-value for the previous test. Interpret.

A survey of 1000 adults from a certain region​ asked, "Do you enjoy shopping for clothing for​ yourself?" The results indicated that 59​% of the females enjoyed shopping for clothing for themselves as compared to 51​% of the males. The sample sizes of males and females were not provided. Suppose that of 600 ​females, 354 said that they enjoyed shopping for clothing for themselves while of 400 ​males, 204 said that they enjoyed shopping for clothing for themselves. Complete parts​ (a) through​ (d) below.

a. Is there evidence of a difference between males and females in the proportion who enjoy shopping for clothing for themselves at the 0.1 level of​ significance? State the null and alternative​ hypotheses, where pi 1 is the population proportion of females that enjoy shopping for themselves and pi 2 is the population proportion of males that enjoy shopping for themselves.

Determine the value of the test statistic.

Determine the critical​ value(s) for this test of hypothesis.

The critical​ value(s) is​ (are) nothing

find the p value

Construct and interpret a 90​% confidence interval estimate for the difference between the proportion of males and females who enjoy shopping for clothing for themselves.

What are the answers to​ (a) through​ (c) if 212 males enjoyed shopping for clothing for​ themselves?

Is there evidence of a difference between males and females in the proportion who enjoy shopping for clothing for themselves at the 0.1 level of​ significance? State the null and alternative​ hypotheses, where pi 1π1 is the population proportion of females that enjoy shopping for themselves and pi 2π2 is the population proportion of males that enjoy shopping for themselves.

Determine the value of the test statistic.

Determine the critical​ value(s) for this test of hypothesis.

The critical​ value(s) is​ (are)

Find the​ p-value and interpret its meaning.

Construct and interpret a 90​% confidence interval estimate for the difference between the proportion of males and females who enjoy shopping for clothing for themselves.

Interpret these correlation coefficients:

•r = -0.84 between total mileage and car resale value

•r = 0.03 between anxiety level and college GPA

•r = 0.56 between age of schoolchildren and reading comprehension

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.