Company A is trying to sell its website to Company B. As part of the sale, Company A claims that the average user of their site stays on the site for 10 minutes. Company B is concerned that the mean time is significantly less than 10 minutes. Company B collects the times (in minutes) below for a sample of 19 users. Assume normality.

Conduct the appropriate hypothesis test for Company B using a 0.08 level of significance.

a) What are the appropriate null and alternative hypotheses?

H₀: μ = 10 versus H_a: μ > 10

H₀: μ = 10 versus H_a: μ < 10    

H₀: x = 10 versus H_a: x ≠ 10

H₀: μ = 10 versus H_a: μ ≠ 10

b) What is the test statistic? Give your answer to four decimal places.  
c) What is the critical value for the test? Give your answer to four decimal places.  
d) What is the appropriate conclusion?

Reject the claim that the mean time is 10 minutes because the test statistic is larger than the critical point.

Fail to reject the claim that the mean time is 10 minutes because the test statistic is larger than the critical point.  

Reject the claim that the mean time is 10 minutes because the test statistic is smaller than the critical point.

Fail to reject the claim that the mean time is 10 minutes because the test statistic is smaller than the critical point.

The sum of deviations of observations around its mean is always zero. Explain this in detail with example?

Lactation promotes a temporary loss of bone mass to provide adequate amounts of calcium for milk production. The paper “Bone Mass Is Recovered from Lactation to Postweaning in Adolescent Mothers with Low Calcium Intakes” gave the following data on total body bone mineral content (TBBMC) (g) for a sample both during lactation (L) and in the postweaning period (P):

                Subject                 L                              P

                1                              1928                       2126      

                2                              2549                       2885

                3                              2825                       2895

                4                              1924                       1942

                5                              1628                       1750

                6                              2175                       2184

                7                              2114                       2164

                8                              2621                       2626

                9                              1843                       2006

                10                           2541                       2627

Estimate the difference between true average TBBMC for the two periods of concrete in a way that conveys information about precision and reliability. Does it appear plausible that the true average TBBMCs for the two periods are identical?

In a survey of a group of​ men, the heights in the​ 20-29 age group were normally​ distributed, with a mean of

69.3 inches and a standard deviation of 2.0 inches. A study participant is randomly selected. Complete parts​ (a) through​ (d) below.

​(a) Find the probability that a study participant has a height that is less than

65 inches.

​)​(b) Find the probability that a study participant has a height that is between

65 and 70 inches

​)​(c) Find the probability that a study participant has a height that is more than 70 inches

Let x be a random variable that represents the pH of arterial plasma (i.e., acidity of the blood). For healthy adults, the mean of the x distribution is μ = 7.4.† A new drug for arthritis has been developed. However, it is thought that this drug may change blood pH. A random sample of 36 patients with arthritis took the drug for 3 months. Blood tests showed that x = 8.6 with sample standard deviation s = 3.0. Use a 5% level of significance to test the claim that the drug has changed (either way) the mean pH level of the blood.

(a) What is the level of significance?


State the null and alternate hypotheses.

H₀: μ = 7.4; H₁: μ > 7.4H₀: μ = 7.4; H₁: μ < 7.4    H₀: μ = 7.4; H₁: μ ≠ 7.4H₀: μ ≠ 7.4; H₁: μ = 7.4H₀: μ > 7.4; H₁: μ = 7.4

(b) What sampling distribution will you use? Explain the rationale for your choice of sampling distribution.

The standard normal, since the sample size is large and σ is unknown.The Student's t, since the sample size is large and σ is unknown.    The Student's t, since the sample size is large and σ is known.The standard normal, since the sample size is large and σ is known.

What is the value of the sample test statistic? (Round your answer to three decimal places.)


(c) Estimate the P-value.

P-value > 0.2500.100 < P-value < 0.250    0.050 < P-value < 0.1000.010 < P-value < 0.050P-value < 0.010

Sketch the sampling distribution and show the area corresponding to the P-value.

(d) Based on your answers in parts (a) to (c), will you reject or fail to reject the null hypothesis? Are the data statistically significant at level α?

At the α = 0.05 level, we reject the null hypothesis and conclude the data are statistically significant.At the α = 0.05 level, we reject the null hypothesis and conclude the data are not statistically significant.    At the α = 0.05 level, we fail to reject the null hypothesis and conclude the data are statistically significant.At the α = 0.05 level, we fail to reject the null hypothesis and conclude the data are not statistically significant.

(e) Interpret your conclusion in the context of the application.

There is sufficient evidence at the 0.05 level to conclude that the drug has changed the mean pH level of the blood.There is insufficient evidence at the 0.05 level to conclude that the drug has changed the mean pH level of the blood.    

1. Create a scatter plot between the children’s BMI and their adoptive parents’ BMI. Format the plot into an APA-styled “figure” (see week 1 video for APA figure format). (3 points total: 1 for correct scatter graph type, 1 for correct data, 1 for APA format- figure number and title/caption)

1. Calculate the mean and standard deviation for the adoptive parents’ BMI. (2 points total: 1 for mean and 1 for SD- deduct .5 if the process is correct but result is wrong)

2. Calculate the Z scores for all the data points for the adoptive parents. (1 point for calculating adoptive parents’ Z scores. Deduct .5 for each error in calculation)

3. Calculate the Pearson’s correlation coefficient r between children’s BMI and their adoptive parents’ BMI. Note that the children’s Z scores have been calculated in Part 1 of this scenario. (2 points total: 1 for work, 1 for r value)

4. Explain the direction and strength of the relationship based on the r. (2 points total: 1 for direction, 1 for strength)

5. What is the proportion of shared variance between children’s BMI and their adoptive parents’ BMI? That is, how much of the variance in the children’s BMI can be predicted from their adoptive parents’ BMI? (2 points total: 1 for work, 1 for result)

6. Based on the two r statistics, what would be the answer to the research question of whether children’s BMI is influenced more by nature or nurture? (1 point)

Please prepare a PowerPoint presentation of the following case.

During the late 1980s, the decline in Akron’s tire industry, inflation, and changes in governmental priorities almost resulted in the permanent closing of the Akron Children’s Zoo. Lagging attendance and a low level of memberships did not help matters. Faced with uncertain prospects of continuing, the city of Akron opted out of the zoo business. In response, the Akron Zoological Park was organized as a corporation to contract with the city to operate the zoo.

The Akron Zoological Park is an independent organization that manages the Akron Children’s Zoo for the city. To be successful, the Zoo must maintain its image as a high-quality place for its visitors to spend their time. Its animal exhibits are clean and neat. The animals, birds, and reptiles are carefully looked after. As resources become available for construction and continuing operations, the Zoo keeps adding new exhibits and activities. Efforts seem to be working, because attendance increased from 53,353 in 1989 to an all-time record of 133,762 in 1994.

Due to its northern climate, the Zoo conducts its open season from mid-April until mid-October. It reopens for one week at Halloween and for the month of December. Zoo attendance depends largely on the weather. For example, attendance was down during the month of December 1995, which established many local records for the coldest temperatures and the most snow. Variations in weather also affect crop yields and prices for fresh animal foods, thereby influencing the costs of animal maintenance.

In normal circumstances, the zoo may be able to achieve its target goal and attract an annual attendance equal to 40% of its community. Akron has not grown appreciably during the past decade. But the Zoo became known as an innovative community resource, and as indicated in the table, annual paid attendance has doubled. Approximately 35% of all visitors are adults. Children account for one-half of the paid attendance. Group admissions remain a constant 15% of zoo attendance.

The Zoo does not have an advertising budget. To gain exposure in its market, the Zoo depends on public service announcements, its public television series, and local press coverage of its activities and social happenings. Many of these activities are but a few years old. They are a strong reason that annual zoo attendance has increased. Although the Zoo is a nonprofit organization, it must ensure that its sources of income equal or exceed its operating and physical plant costs. Its continued existence remains totally dependent on its ability to generate revenues and to reduce its expenses.

Source: Professor F. Bruce Simmons III, University of Akron.

Questions

1. The president of the Akron Zoo asked you to calculate the expected gate admittance figures and revenues for both 1999 and 2000. Would simple linear regression analysis be the appropriate forecasting technique?
2. What factors other than admission price influence annual attendance and should be considered in the forecast?

Since 2007, the American Psychological Association has supported an annual nationwide survey to examine stress across the United States. A total of 360 Millennials (18- to 33-year-olds) were asked to indicate their average stress level (on a 10-point scale) during a month. The mean score was 5.4. Assume that the population standard deviation is 2.3.

(a) Give the margin of error for a 95% confidence interval. (Round your answer to three decimal places.)

Find the 95% confidence interval for this sample. (Round your answers to three decimal places.)

(b) Give the margin of error for a 99% confidence interval. (Round your answer to three decimal places.)

Find the 99% confidence interval for this sample. (Round your answers to three decimal places.)

Suppose the heights of 18-year-old men are approximately normally distributed, with mean 72 inches and standard deviation 6 inches.

(a) What is the probability that an 18-year-old man selected at random is between 71 and 73 inches tall? (Round your answer to four decimal places.)


(b) If a random sample of eleven 18-year-old men is selected, what is the probability that the mean height x is between 71 and 73 inches? (Round your answer to four decimal places.)

We wish to test the hypothesis that μ≥0 at the 4% level using a sample of 60 observations. The rejection region for this test is:

• Below -1.75
• Above 1.75
• Below -2.05
• Above 2.05

Things to note

The mean time it takes a man to run a mile is known to be 25 minutes.

A running company has developed a shoe that claim provides faster times time. Scientists tested the new shoe on a sample of 25 individuals.

For this sample, the mean mile time was 20 mins.

The population standard deviation for the mile is known to be 7 minutes.

A level of significance of .01 is to be used to test if the new shoe provides faster mile times

Mean = 25 min

Sample size 25

Sample average time taken 20 minutes

Standard deviation 7 minutes.

A level of significance of .01

1.            State the null and alternative hypotheses

2.            Determine the critical value (cut-off point) for the test.

3.            a. Draw a diagram of the sampling distribution used to perform the test.

b. Label the horizontal axis of your diagram.   

c. Locate the critical value on your diagram.    

Jeff is willing to invest $6,000 in buying shares and bonds of a company to gain maximum returns. From his past experience, he estimates the relationship between returns and investments made in this company to be:

R = –2S² – 9B² – 4SB + 20S + 30B.        

where,
R = total returns in thousands of dollars
S = thousands of dollars spent on Shares
B = thousands of dollars spent on Bonds
Jeff would like to develop a strategy that will lead to maximum return subject to the restriction provided on the amount available for investment.

a. What is the value of return if $4,000 is invested in shares and $2,000 is invested bonds of the company?
b. Formulate an optimization problem that can be solved to maximize the returns subject to investing no more than $6,000 on both shares and bonds.
c. Determine the optimal amount to invest in shares and bonds of the company. How much return will Jeff gain? Round all your answers to two decimal places.

What price do farmers get for their watermelon crops? In the third week of July, a random sample of 41 farming regions gave a sample mean of x = $6.88 per 100 pounds of watermelon. Assume that σ is known to be $1.94 per 100 pounds.

(a) Find a 90% confidence interval for the population mean price (per 100 pounds) that farmers in this region get for their watermelon crop. What is the margin of error? (Round your answers to two decimal places.)

(b) Find the sample size necessary for a 90% confidence level with maximal error of estimate E = 0.37 for the mean price per 100 pounds of watermelon. (Round up to the nearest whole number.)
farming regions

(c) A farm brings 15 tons of watermelon to market. Find a 90% confidence interval for the population mean cash value of this crop. What is the margin of error? Hint: 1 ton is 2000 pounds. (Round your answers to two decimal places.)

Complete the following statements by typing your answers in the spaces provided. If you are asked to determine the probabilities, state your answers to 4 decimal places. If you are asked to determine a value of Y, state your answers to 2 or 3 decimal places. Because you will be typing in your answers, I cannot ask you to draw diagrams as I have done in my previously posted practice finals and solutions to examples, I suggest when you are working on your answers on scrap pieces of paper (or a print out of the exam sheets), draw the diagrams. You are more likely to get the right answer if you use diagrams. For each of these statements I am asking you fill in more than one blank so that I can give you part marks if your intermediate calculation is correct but your final calculation is wrong.  

When answering each of the following, the random variable Y is normally distributed with a mean of 65 and a standard deviation of 4.

1. The value of z for being able to determine P(Y ≤ 62) is _______

The P(Y ≤ 62) is ________

2. The 2 values of z for being able to determine P( 69 ≤ Y ≤ 74) are _______ and ________

The P( 69 ≤ Y ≤ 74) is _________

3. The value of z for being able to determine P(Y ≥ 72) is _______

The P(Y ≥ 72) is ________

4. The value of z for being able to determine the value of y such that 10% of the values Y are less than that y

Is ________

               The value of y such that 10% of the values Y are less than that y is _________