In this problem, assume that the distribution of differences is approximately normal. Note: For degrees of freedom d.f. not in the Student's t table, use the closest d.f. that is smaller. In some situations, this choice of d.f. may increase the P-value by a small amount and therefore produce a slightly more "conservative" answer.

At five weather stations on Trail Ridge Road in Rocky Mountain National Park, the peak wind gusts (in miles per hour) for January and April are recorded below.

Does this information indicate that the peak wind gusts are higher in January than in April? Use α = 0.01. (Let

d = January − April.)(a) What is the level of significance?


State the null and alternate hypotheses. Will you use a left-tailed, right-tailed, or two-tailed test?

H₀: μ_d = 0; H₁: μ_d ≠ 0; two-tailed H₀: μ_d = 0; H₁: μ_d > 0; right-tailed     H₀: μ_d = 0; H₁: μ_d < 0; left-tailed H₀: μ_d > 0; H₁: μ_d = 0; right-tailed

(b) What sampling distribution will you use? What assumptions are you making?

The standard normal. We assume that d has an approximately uniform distribution. The Student's t. We assume that d has an approximately uniform distribution.     The standard normal. We assume that d has an approximately normal distribution. The Student's t. We assume that d has an approximately normal distribution.

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

Anystate Auto Insurance Company took a random sample of 370 insurance claims paid out during a 1-year period. The average claim paid was $1535. Assume σ = $254.

Find a 0.90 confidence interval for the mean claim payment. (Round your answers to two decimal places.)

Find a 0.99 confidence interval for the mean claim payment. (Round your answers to two decimal places.)

A Drug Company wishes to do a clinical trial on a new antidepressant drug, “summer”. Four groups of clinically depressed participants receive: 0 mg, 5 mg, 10 mg, and 15 mg of “summer”.  Depressed patients are not active so activity level as measured by the Turkey Activity Sale (TAS) was used after a two-month trial. Results were:

            Activity Level (TAS)

A.        State the Independent Variable and the Dependent Variable.

B.        State the null hypothesis in words and symbols.

C.        Compute the appropriate statistic.

D.        What is your decision?

E.         State the full conclusion in words, after computing, if necessary multiple comparisons.

Suppose the number of cars in a household has a binomial distribution with parameters n = 12, and p = 10 %. Find the probability of a household having: (a) 1 or 5 cars (b) 3 or fewer cars (c) 9 or more cars (d) fewer than 5 cars (e) more than 3 cars

A developmental psychologist is examining problem solving ability for grade school children. Random samples of 5-year-old, 6-year-old, and 7-year-old are obtained and a set of problems are given to them. The number of errors is reported below.

Number of errors

A.        State the Independent Variable and the Dependent Variable.

B.        State the null hypothesis in words and symbols.

C.        Compute the appropriate statistic.

D.        What is your decision?

E.         State the full conclusion in words, after computing, if necessary multiple comparisons .

The birth weights for two groups of babies were compared in a study. In one group the mothers took a zinc supplement during pregnancy. In another group, the mothers took a placebo. A sample of 227 babies in the zinc group had a mean birth weight of 3255 grams. A sample of 276 babies in the placebo group had a mean birth weight of 30023002 grams. Assume that the population standard deviation for the zinc group is 708 grams, while the population standard deviation for the placebo group is 661 grams. Determine the 90%  confidence interval for the true difference between the mean birth weights for "zinc" babies versus "placebo" babies.

Step 2 of 3 :  

Calculate the margin of error of a confidence interval for the difference between the two population means. Round your answer to six decimal place

1) What is a hypothesis, a hypothesis test, a null hypothesis and an alternative hypothesis?

2) What is a P-value, critical value and a test statistic? Provide an example of each and describe how they are used to test claims.

3) When conducting a hypothesis test, what is the difference between the P-value method and the critical-value method?

4) List and explain all the steps for performing a hypothesis test.

Directions: write the finding of these questions in a short passage around 200-300 words

The stem diameter of wheat is important because easy breakage of the wheat can interfere with harvesting the crop. The diameter of wheat is known to be normally distributed with a mean of 1.9 mm. An agronomist hypothesizes that the new fertilizer being used is increasing plant stem diameter. After 5 days from the flowering of the wheat, the agronomist measures the diameters (mm) of the plants. What can the agronomist conclude with an α of 0.01? The wheat diameters are as follows:
1.8, 2.6, 2.4, 1.7, 2.3, 2.5, 1.9, 2, 3, 1.2.

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--- weeks stem diameter the new fertilizer sample of wheat grown average wheat
Sample:
---Select--- weeks stem diameter the new fertilizer sample of wheat grown average wheat

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.)
critical value =  ; test statistic =
Decision:  ---Select--- Reject H0 Fail to reject H0

d) If appropriate, compute the CI. If not appropriate, input "na" for both spaces below.
[  ,  ]

e) 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

f) Make an interpretation based on the results.

The wheat grown with the new fertilizer has a significantly larger diameter than average wheat.

The wheat grown with the new fertilizer has a significantly smaller diameter than average wheat.    

The wheat grown with the new fertilizer did not have a significantly different diameter than average wheat.

A researcher studies the effect of the herbal stimulant Buttercup on short-term memory; she randomly divides a sample of 32 into four (4) groups.  Each group receives 0 mg, 500 mg, 1000 mg and 1500 mg respectively and is then tested on their short term memory span.  She finds:

                        NUMBER OF ITEMS REMEMBERED (MEMORY SPAN)

            0.0 mg             500 mg                        1000 mg                      1500 mg          

            8                      7                                  10                                4

            9                      6                                  15                                5

            7                      9                                  14                                2

            7                      8                                  14                                4

            8                      8                                  17                                3

            10                    6                                  13                                8

            6                      12                                9                                  7

            7                      9                                  12                                9

A.        State the Independent Variable and the Dependent Variable.

B.        State the null hypothesis in words and symbols.

C.        Compute the appropriate statistic.

D.        What is your decision?

E.         State the full conclusion in words, after computing, if necessary multiple comparisons.

Weights of 50 babies at birth.

Write at least a 1-Page Report Open a Word Document

Introduction--Provide a description of your topic and cite where you found your data. Sample Data—Include a 5x10 table including your 50 values in your report. You must provide ALL of your sample data.

Problem Computations—For the topic you chose, you must answer the following: Determine the mean and standard deviation of your sample. Find the 80%, 95%, and 99% confidence intervals. Make sure to list the margin of error for the 80%, 95%, and 99% confidence interval. Create your own confidence interval (you cannot use 80%, 95%, and 99%) and make sure to show your work. Make sure to list the margin of error.

Problem Analysis—Write a half-page reflection. What trend do you see takes place to the confidence interval as the confidence level rises? Explain mathematically why that takes place. Provide a sentence for each confidence interval created in part c) which explains what the confidence interval means in context of topic of your project. Explain how Part I of the project has helped you understand confidence intervals better? How did this project help you understand statistics better?

EXPERIMENT 1    

Part 1:

Dr. Saunders wanted to know whether adolescents who had restricted television viewing time studied more than adolescents who had unlimited television viewing time. She recruited a small sample of children aged 12 to 17 years old; some of these children were allowed limited access to their home televisions, and others were allowed unlimited access. She obtained the following studying time data (in minutes) fore the two groups:

Enter these data into SPSS in the appropriate manner for the type of analysis you will conduct. Label the columns appropriately.

After you answer questions about the appearance of the information in Data View, you will conduct the appropriate statistical test.

1. Enter all the numbers or words you see in the first column in SPSS data view in the same order they are shown in that column.

Question 1 options:

Blank # 1

Blank # 2

Blank # 3

Blank # 4

Blank # 5

Blank # 6

Blank # 7

Blank # 8

Blank # 9

Blank # 10

Blank # 11

Blank # 12

2. What text goes in the header of the first column?

3. Enter all the numbers or words you see in the second column in SPSS data view in the same order they are shown in that column.

Question 3 options:

Blank # 1

Blank # 2

Blank # 3

Blank # 4

Blank # 5

Blank # 6

Blank # 7

Blank # 8

Blank # 9

Blank # 10

Blank # 11

Blank #12

4. What text goes in the header of the second column?

Part 2:

Using SPSS compute the appropriate statistical test to determine whether there is a difference in study time between the children with limited vs. unlimited television viewing. Fill in the empty cells based on the output of the statistical test you conducted.

Write your answer to the same number of decimal places as you see in your SPSS output.

What is the critical value t* for a 99% confidence interval when n = 20?

1. What is the “Prime Rate-1 Month Prior” for the following Countries:
   1. Canada- 2.45
   2. United States-3.25
   3. United Kingdom-0.66
   4. European Central Back
   5. Japan

What methodology was used to collect and analyze the data? Did the source collect the data? When was the data collected? Why was the data originally collected? How dependable is the data's source?

Plz answer all the questions i'm boutta fail this class

Suppose that for a typical FedEx package delivery, the cost of the shipment is a function of the weight of the package. You find out that the regression equation for this relationship is (cost of delivery) = 3.603*(weight) + 4.733. If a package you want to ship weighs 44 ounces, what would you expect to pay for the shipment?

A. 163.27

B.158.53

C.We do not know the observations in the data set, so we cannot answer that question.

D.10.9

E. 211.85

Suppose that for a typical FedEx package delivery, the cost of the shipment is a function of the weight of the package. You find out that the regression equation for this relationship is (cost of delivery) = 1.971*(weight) + 7.071. Interpret the slope.

A.When weight increases by 1 pound, cost of delivery increases by 7.071 dollars.

B.We are not given the dataset, so we cannot make an interpretation

C.When cost of delivery increases by 1 dollar, weight increases by 1.971 pounds.

D.When cost of delivery increases by 1 dollar, weight increases by 7.071 pounds.

E. When weight increases by 1 pound, cost of delivery increases by 1.971 dollars.

Suppose that a researcher studying the weight of female college athletes wants to predict the weights based on height, measured in inches, and the percentage of body fat of an athlete. The researcher calculates the regression equation as (weight) = 4.459*(height) + 0.85*(percent body fat) - 89.236. If a female athlete is 61 inches tall, has a 22 percentage of body fat, and a weight of 166.425, the residual is -35.038. Choose the correct interpretation of the residual.

A. The weight of the athlete is 35.038 pounds less than what we would expect.

B. The height of the athlete is 35.038 inches less than what we would expect.

C. The height of the athlete is 35.038 inches larger than what we would expect.

D.The weight of the athlete is 166.425 pounds less than what we would expect.

E.The weight of the athlete is 35.038 pounds greater than what we would expect.

While attempting to measure its risk exposure for the upcoming year, an insurance company notices a trend between the age of a customer and the number of claims per year. It appears that the number of claims keep going up as customers age. After performing a regression, they find that the relationship is (claims per year) = 0.28*(age) + 5.17. If a customer is 41 years old and they make an average of 12.95 claims per year, what is the residual?

A.24.35

B.-28.05

C.3.7

D.28.05

E. -3.7

Suppose that in a certain neighborhood, the cost of a home (in thousands) is proportional to the size of the home in square feet. The regression equation quantifying this relationship is found to be (price) = 0.024*(size) + 39.993. You look more closely at one of the houses selected. The house is listed as having 2033.702 square feet and is listed at a price of $104.498 (thousand). The residual is 15.696. Interpret this residual in terms of the problem.

A.The price of the house is 15.696 thousand dollars larger than what we would expect.

B. The price of the house is 104.498 thousand dollars larger than what we would expect.

C. The price of the house is 15.696 thousand dollars less than what we would expect.

D. The square footage is 15.696 square feet larger than what we would expect.

E. The square footage is 15.696 square feet less than what we would expect.

Suppose that a researcher studying the weight of female college athletes wants to predict the weights based on height, measured in inches, and the percentage of body fat of an athlete. The researcher calculates the regression equation as (weight) = 4.715*(height) + 1.108*(percent body fat) - 90.653. If a female athlete is 63 inches tall and has a 15 percentage of body fat, what is her expected weight?

A. Not enough information

B. 404.318

C.313.665

D. 49.876

E.223.012

Suppose the sales (1000s of $) of a fast food restaurant are a linear function of the number of competing outlets within a 5 mile radius and the population (1000s of people) within a 1 mile radius. The regression equation quantifying this relation is (sales) = 1.526*(competitors) + 6.09*(population) + 7.226. Suppose the sales (in 1000s of $) to be of a store that has 5 competitors and a population of 7 thousand people within a 1 mile radius are 54.151 (1000s $). What is the residual?

A. -3.335

B. 52.486

C. 3.335

D. Not enough information

Confidence Intervals

1. In a random sample of 1100 American adults it was found that 320 had hypertension (high-blood pressure). The US Department of Health and Human Services (HHS) wants the population proportion of hypertension to 16% by 2022.

   1. Find the 95% confidence interval for the proportion of all adult Americans that have hypertension.

   2. Interpret the confidence interval in the words of the problem.

   3. Find the error bound.

   4. Does this data and analysis provide evidence that the population proportion of hypertension is different from the HHS target value? Justify!