Calculate the test statistic. A research company claims that no more than 55% of Americans regularly watch FOX News. You decide to test this claim and ask a random sample of 425 Americans if they watch this network regularly. Of the 425 sampled, 255 respond yes. Calculate the test statistic for the hypothesis test. a) -2.07 b) 1.645 c) -1.96 d) 2.07 e) None of the above.

4. An airline sells 338 tickets for a flight to Manila which has 335 seats. It is estimated that 98% of all ticketed passengers show up for the flight. Find the probability that the flight will depart with (at least one) empty seats? (10)

1. Which of the following statements best describes a sampling distribution?

Select one:

a. It is the distribution of the values of a variable in the population from which the sample is taken

b. It is the distribution of the values of a statistic that resembles the normal distribution when the sample size is large

c. It is the distribution of the values of a statistic calculated from 1000 simple random samples displayed in a histogram.

d. It is the distribution of the values of a particular variable that are observed in a random sample.

2. The weight of extra-large egg has a Normal distribution with a mean of 3 oz and a standard deviation of 0.1 oz.

What is the sampling distribution of the mean weight of extra-large egg (i.e., the distribution of the sample mean weight of an egg in a randomly selected carton of a dozen eggs (i.e., 12 eggs))?     

Select one:

a. N(12,1)

b. N(3, 0.1)

c. N(3, 0.03)

d. N(3, 0.2)

3. The manager at a movie theater would like to estimate the true mean amount of money spent by customers on popcorn only. He selects a simple random sample of 26 receipts and calculates a 92% confidence interval for true mean to be ($12.45, $23.32). The confidence interval can be interpreted to mean that, in the long run,                   

Select one:

a. 92% of all customers who buy popcorn spend between $12.45 and $23.22

b. 92% of similarly constructed intervals would contain the population mean

c. 92% of similarly constructed intervals would contain the sample mean

4. A population variable has a distribution with mean µ = 25 and variance σ² is 256. From this population a simple random sample of n observations is to be selected and the mean of the sample values calculated. If the population variable is known to be Normally distributed and the sample size is to be n = 25, what is the probability that the sample mean will be between 20.5 and 31.50, i.e., P(20.5 ≤ x-bar ≤ 31.5)?

5. Since confidence intervals are based on the sampling distribution of the sample mean, it is possible to form confidence intervals when sampling from slightly skewed distributions due to the central limit theorem

Select one:

True

False

6. The heights of a simple random sample of 200 male high school sophomores in a midwestern state are measured. The sample mean (x-bar) is 70 inches. Suppose that the heights of male high school sophomores follow a Normal distribution with a standard deviation is 5 inches.    

What is a 99% confidence interval for the population mean μ?

Select one:

a. (59.46, 72.94)

b. (69.09, 70.91)

c. (65.67, 66.73)

d. (58.16, 74.24)

7. The heights of a simple random sample of 200 male high school sophomores in a midwestern state are measured. The sample mean (x-bar) is 70 inches. Suppose that the heights of male high school sophomores follow a Normal distribution with a standard deviation of σ is 5 inches.

Suppose the heights of a simple random sample of 100 male sophomores were measured instead of 200. Which of the following statements is true?  

Select one:

a. The margin of error for the 95% confidence interval would decrease

b. The margin of error for the 95% confidence interval would increase

c. The standard deviation would decrease

1. What is the response rate of an online survey sent to 650 email recipients, where 100 email addresses were ineligible, 400 recipients responded to the survey, and 150 refused to participate? (Show all your work)

2.  A department store manager believes that at least half of the households in a test market city contain at least one adult who has visited the store since the new layout was introduced. To conduct online surveys, a researcher working with this manager has purchased access to a 1,100 online panel with members located in the target area. The researcher asked the following question to the contacted respondent "Has any adult in this household visit XYZ department store in the previous month?". Here are the final results of the online panel surveys.

Completed surveys 426

Refusals 260

No Contact 0

Ineligible surveys 292

Nonworking emails 122

What is the response rate with eligibility requirements? Show all your work.

3. Knowing that you need a sample pool of 1019 students to ultimately get about 500 students in your sample, you are in a position to draw a systematic sample from the student directory at your university. Further, 9,500 students are listed in the directory. What is the sampling interval? Interpret your results. Show all your work

The age distribution of the Canadian population and the age distribution of a random sample of 455 residents in the Indian community of a village are shown below.

Use a 5% level of significance to test the claim that the age distribution of the general Canadian population fits the age distribution of the residents of Red Lake Village.

(a) What is the level of significance?


State the null and alternate hypotheses.

H₀: The distributions are the same.
H₁: The distributions are the same.H₀: The distributions are the same.
H₁: The distributions are different.    H₀: The distributions are different.
H₁: The distributions are different.H₀: The distributions are different.
H₁: The distributions are the same.

(b) Find the value of the chi-square statistic for the sample. (Round your answer to three decimal places.)


Are all the expected frequencies greater than 5?

YesNo    

What sampling distribution will you use?

Student's tchi-square    binomialuniformnormal

What are the degrees of freedom?


(c) Estimate the P-value of the sample test statistic.

P-value > 0.1000.050 < P-value < 0.100    0.025 < P-value < 0.0500.010 < P-value < 0.0250.005 < P-value < 0.010P-value < 0.005

(d) Based on your answers in parts (a) to (c), will you reject or fail to reject the null hypothesis that the population fits the specified distribution of categories?

Since the P-value > α, we fail to reject the null hypothesis.Since the P-value > α, we reject the null hypothesis.    Since the P-value ≤ α, we reject the null hypothesis.Since the P-value ≤ α, we fail to reject the null hypothesis.

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

At the 5% level of significance, the evidence is insufficient to conclude that the village population does not fit the general Canadian population.At the 5% level of significance, the evidence is sufficient to conclude that the village population does not fit the general Canadian population.  

You are interested in examining the factors that determine the average length of stay in a hospital across provinces. You collect data on the following variables:
Y = province-wide average hospital stay
X₂ = median provincial income
X₃ = 1 if the province is one of the Atlantic provinces, 0 otherwise
X₄ = 1 if the province is in Quebec or Ontario, 0 otherwise
X₅ = 1 if the province is in the Prairies, 0 otherwise
X₆ = 1 if the province is BC or Alberta, 0 otherwise

You run the following regression Y = β₁ + β₂X₂ + β₃X₃ + β₄X₄ + β₅X₅. How much longer would we expect to stay in a hospital in the Atlantic provinces than in a hospital in Ontario or Quebec?

A recent study found that 56% of workers between the ages of 20-29 cash out their retirement accounts when they lose their jobs or move to a new employer. Complete parts a through e below based on a random sample of 14 workers between the ages of 20-29 who lost their jobs or changed employers.

1. What is the probability that exactly 3 workers cashed out their retirement accounts? The probability is_________. (Round to four decimal places as needed.)
2. What is the probability that all 14 workers from the sample cashed out their retirement accounts? The probability is_________.(Round to four decimal places as needed.)
3. What is the probability that 11 or fewer workers cashed out their retirement accounts? The probability is _________(Round to four decimal places as needed.)
4. What are the mean and standard deviation for this distribution?
   1. The mean is _________(Type an integer or a decimal.)
   2. The standard deviation is ___________. (Round to four decimal places as needed.

1. According to well-developed national norms, the mean of scores on the OB Anxiety scale among American adults equals 50 and the standard deviation of scores on this inventory equals 15. A researcher wants to assess whether adults living in Canada differ in anxiety from American adults. She has no a priori hypothesis about whether Canadians have higher or lower values (i.e., the key thing of interest at this stage is whether the Canadians simply differ from Americans) She administers the OB scale to 121 randomly sampled Canadian adults. The mean OB score for this sample is 52.5. She assumes that the population standard deviation of Canadian scores is the same as the population standard deviation of American scores.

a. What are her null and alternative hypotheses?

b. Conduct a statistical test of the null hypothesis.

Using the formula Y_x=Ax^b, where:

Y_x = the cost of unit x (dependent variable)

A = the theoretical cost of unit 1 (a.k.a. T1)

x = the unit number (independent variable)

b = a constant representing the slope (slope = 2^b)

Calculate the unit theory first theoretical unit cost (T1) if the production quantity was 270 and the average unit cost was $2.74. Assume a 78% learning rate.

The following table summarizes the results of 220 drug tests.

1. P(uses drugs) =
   

2. P(tested negative) =
   

3. P(tested negative | uses drugs) =
   

4. P(uses drugs | tested negative) =
   

5. P(tested negative | does not use drugs) =

3)    Which of the following questions can be answered based on a normal model?Explain. (You do not need to answer the questions, just determine if a normal model is appropriate.)
a)    According to the growth charts produced by the World Health Organization, one-month-old girls have a mean head circumference of 36.55cm and a standard deviation of 1.17 cm. In general, body measurements in a large population can be modeled by a normal curve.
In a study of health conditions in a county with a high poverty rate, researchers find that a random sample of 25 one-month-old girls have a mean head circumference of 36cm. Does this sample provide strong evidence that the mean head circumference for the population of one-month-old girls in this county is unusually small?
b)    According to the US Census Bureau 2014 Annual Social and Economic Supplement, the mean household income in the United States was $72,641. Previous studies suggest that the standard deviation is about $35,000. Income data is skewed strongly to the right.
We are interested in determining whether the mean household income is higher in our county. We randomly sample 25 households and determine that the mean income is $65,000. Does this sample provide strong evidence that the mean income is lower in our county?

1. In the US, 45% of the population has blood type O, 40% have blood type A, 11% have blood type B, and 4 percent have blood type AB. Two individuals are chosen independently.  

a. What is the probability they both have blood type AB?

b. What is the probability they both have blood type B?

c. In what situation must you consider conditional probabilities?

2. A large national sample of health care visits to the VA indicates that 9.1% of veterans over age 60 have chronic kidney disease. The rate is 14.1% among veterans in their 60s with diabetes and 6.4% among veterans in their 60s without diabetes.

a. P(chronic kidney disease) =

b. P(chronic kidney disease | diabetes) =

c. P(chronic kidney disease | no diabetes) =

About 100 years ago, physicists were working to determine the speed of light. The results of 25 independent measurements gave an average of 299.796 million meters/second with a standard deviation of 0.004 million meters/second. Assume the distribution of measurements was not strongly skewed.

What type of inference is most appropriate given the goal of the research?

A.Hypothesis test

B.Confidence interval

C.No inference is needed

Andalus Furniture Company has two manufacturing plants, one at Aynor and another at Spartanburg. The cost in dollars of producing a kitchen chair at each of the two plants is given here.

Aynor: Cost = 66Q1 + 6Q1² + 105
Spartanburg: Cost = 20Q2 + 2.5Q2² + 156

Andalus needs to manufacture a total of 50 kitchen chairs to meet an order just received. How many chairs should be made at Aynor and how many should be made at Spartanburg in order to minimize total production cost? When required, round your answers to the nearest dollar.

The optimal solution is to produce chairs at Aynor for a cost of $   and chairs at Spartanburg for a cost of $  . The total cost is $  .