For this problem, carry at least four digits after the decimal in your calculations. Answers may vary slightly due to rounding.

A random sample of 5300 permanent dwellings on an entire reservation showed that 1690 were traditional hogans.

(a) Let p be the proportion of all permanent dwellings on the entire reservation that are traditional hogans. Find a point estimate for p. (Round your answer to four decimal places.)


(b) Find a 99% confidence interval for p. (Round your answer to three decimal places.)

Give a brief interpretation of the confidence interval.

1% of the confidence intervals created using this method would include the true proportion of traditional hogans.1
% of all confidence intervals would include the true proportion of traditional hogans.     
99% of all confidence intervals would include the true proportion of traditional hogans.
99% of the confidence intervals created using this method would include the true proportion of traditional hogans.

(c) Do you think that np > 5 and nq > 5 are satisfied for this problem? Explain why this would be an important consideration.

No, the conditions are not satisfied. This is important because it allows us to say that p̂ is approximately binomial.
Yes, the conditions are satisfied. This is important because it allows us to say that p̂ is approximately normal.     
Yes, the conditions are satisfied. This is important because it allows us to say that p̂ is approximately binomial.
No, the conditions are not satisfied. This is important because it allows us to say that p̂ is approximately normal.

A group of 51 college students from a certain liberal arts college were randomly sampled and asked about the number of alcoholic drinks they have in a typical week. The purpose of this study was to compare the drinking habits of the students at the college to the drinking habits of college students in general. In particular, the dean of students, who initiated this study, would like to check whether the mean number of alcoholic drinks that students at his college in a typical week differs from the mean of U.S. college students in general, which is estimated to be 4.73.

The group of 51 students in the study reported an average of 4.35 drinks per with a standard deviation of 3.88 drinks.

Find the p-value for the hypothesis test.  

The p-value should be rounded to 4-decimal places.

A company received a shipment from a supplier. The supplier company said the mean height of a tire is 21 inches and a standard deviation is 3 inches. The company is planning to choose 55 tires at random. What is the sample mean between 20 and 22? How many tires are likely to be taller than 25 iches?

Gru's schemes have a 9% chance of succeeding. An agent of the Anti-Villain League obtains access to a simple random sample of 1100 of Gru's upcoming schemes. Find the probability that... (Answers should be to four places after the decimal, using chart method, do NOT use the continuity correction):

...less than 101 schemes will succeed:

...more than 95 schemes will succeed:

...between 95 and 101 schemes will succeed:

...less than 8.5% of schemes will succeed:

...more than 9.5% of schemes will succeed:

...between 8.5% and 9.5% of schemes will succeed:

How are the population mean and the mean of the sampling distribution of the mean related?

-What is the standard error of the mean? What does it measure?

-What effect does increasing sample size have on the size of the standard error?

-What does the central limit theorem state?

-What are the units of a z-score?

-How are z-scores related to standard deviation and the mean?How are they interpreted?

-Is the α always a certain value, or is it up to the investigator?

-Is the p-value of a calculated statistic a designated number, or is it up to the investigator?

-How can we reduce Type I error?

-In hypothesis testing, how can you reach a decision about the null hypothesis by comparing yourcalculated statistic to the appropriate critical value?

-In hypothesis testing, how can you reach a decision about the null hypothesis by comparing the p-value from your calculated statistic to your alpha level?

-What is the interpretation of a confidence interval?

-What determines the width of a confidence interval? How is it affected by sample size and α?

-What do we use hypothesis testing to determine? What do we use confidence intervals to determine?

-When can we use z-tests and when do we have to, instead, use t-tests?

-How does the t-distribution compare to the z-distribution?

-What does it mean when two samples are “related”?

-Given two related samples, what are “repeated measures”? What are “matched pairs”?

13. A study published in 2008 by researchers at UT Austin found that 124 out of 1,923 U of T females had over $6,000 in credit card debt while 65 out of 1,236 males had over $6,000 in credit card debt. Test using 0.05, if there is evidence that the proportion of female students at U of T with more than $6,000 credit card debt.

a. Verify that the sample size is large enough in each group to use the normal distribution to perform a hypothesis test for a difference in two groups.

b. Write out the null and alternative hypotheses.

c. Find the value of the pooled standard error. Round to 4 decimal places.

d. The test statistic for this sample is z=1.77, find the p-value. Round to 4 decimal places.

e. Make a formal decision for the hypothesis test based on your p-value in part d. Interpret your decision in the context of the original question.

Refer to the accompanying data​ table, which shows the amounts of nicotine​ (mg per​ cigarette) in​ king-size cigarettes,​ 100-mm menthol​ cigarettes, and​ 100-mm nonmenthol cigarettes. The​ king-size cigarettes are​ nonfiltered, while the​ 100-mm menthol cigarettes and the​ 100-mm nonmenthol cigarettes are filtered. Use a 0.05 significance level to test the claim that the three categories of cigarettes yield the same mean amount of nicotine. Given that only the​ king-size cigarettes are not​ filtered, do the filters appear to make a​ difference?

King-Size   100-mm_Menthol   Filtered_100-mm_Nonmenthol
1.4   1.2   0.7
1.1   0.9   1.0
1.0   1.2   0.4
1.1   0.9   1.1
1.4   1.2   1.1
1.2   1.3   0.7
1.3   0.9   1.0
1.0   1.1   1.2
1.2   0.9   0.8
1.2   0.8   0.9

1. Determine the null and alternative hypotheses.

2. Find the F statistic.

3. Find the P value.

4. What is the conclusion for this hypothesis test?

A. Reject H 0. There is insufficient evidence to warrant rejection of the claim that the three categories of cigarettes yield the same mean amount of nicotine.

B. Fail to reject H 0. There is insufficient evidence to warrant rejection of the claim that the three categories of cigarettes yield the same mean amount of nicotine.

C. Reject H 0. There is sufficient evidence to warrant rejection of the claim that the three categories of cigarettes yield the same mean amount of nicotine.

D. Fail to reject H 0. There is sufficient evidence to warrant rejection of the claim that the three categories of cigarettes yield the same mean amount of nicotine

5. Do the filters appear to make a difference?

A. ​No, the filters do not appear to make a difference because there is sufficient evidence to warrant rejection of the claim.

B. No, the filters do not appear to make a difference because there is insufficient evidence to warrant rejection of the claim.

C. The results are inconclusive because the​ king-size cigarettes are a different size than the filtered cigarettes.

D. Given that the king dash size cigarettes have the largest mean comma it appears that the filters do make a difference left parenthesis although this conclusion is not justified by the results from analysis of variance right parenthesis .

"In Excel, if you had a spreadsheet containing four variables (date, product_type, quantity, and unit_price) and your boss asked you to calculate the total revenue generated by Product A between Thanksgiving and New Years, what formula would you use?"

1. COUNT(()
2. COUNTIFS()
3. SUMIF()
4. SUMIFS()

Question 2

"In regression, what is the best description of a residual?"

Select the correct answer

1. The square of actual values.
2. The predicted values.
3. Error.
4. The sum of the squared difference between the predicted and actual values.

Question 3

"When data is skewed, which statistic best represents the typical value of the data?"

Select the correct answer

1. mean
2. median
3. average
4. None of the above

Question 4

Clustering falls best under which type of analysis?

Select the correct answer

1. descriptive
2. predictive
3. prescriptive
4. None of the above.

Question 5

What type of variable is age?

Select the correct answer

1. ordinal
2. interval
3. categorical
4. continuous

Question 6

What is a distribution?

Select the correct answer

1. A symmetric curve that shows how many observations are in a dataset.
2. A curve that describes the possible values for a variable and how often they occur.
3. A function that describes the number of variables in a dataset.
4. A function that transforms values from one domain to another.

Question 7

What type of plot is best for exploring the correlation between two variables?

Select the correct answer

5. scatterplot
6. barchart
7. line graph
8. bubble chart

Question 8

"In Excel, which formula could be used to merge a column into a dataset?"

Select the correct answer

1. INDEX()
2. HLOOKUP()
3. VLOOKUP()
4. JOIN()

Question 9

Data visualization falls best under which type of analysis?

Select the correct answer

1. descriptive
2. predictive
3. prescriptive
4. None of the above.

Question 10

How do you address multicollinearity?

Select the correct answer

1. Remove one of every two highly correlated IVs
2. Remove all of the highly correlated IVs.
3. Standardize your data to reduce the correlation.
4. Remove the IV.

Question 11

A distribution of a discrete variable is called a histogram.

1. True
2. False

Question 12

Which of the following is true?

Select the correct answer

1. A distribution is always symmetrical.
2. The total area under a distribution curve is always equal to one.
3. Only continuous variables can have distributions.
4. Distributions describe the probability that a variable will take on specific values.
5. Both B and D are correct

2. Listed below are the costs in dollars of flights from New York (JFK) to San Francisco (SFO) for different airlines. Use a 0.01 significance level to test the claim that flights scheduled one day in advance cost more than flights scheduled 30 days in advance. SCHEDULE US Air Virgin Delta United American Alaska Northwest 1 day in advance 456 614 628 1088 943 567 536 30 days in advance 244 260 264 264 278 318 280 a) CLAIM: (IN WORDS) ________________________________________________________________________________________________________ b) CLAIM: (IN EQUATION FORM) ________________________________________________________________________________________________________ c) DETERMINE THE HYPOTHESES H0: H1：________________________________________________________________________________________________________ d) DRAW THE DISTRIBUTION - LABEL THE CRITICAL VALUE(S)

e) CALCULATE THE TEST STATISTIC and include the test statistic on the graph above. ______________________________________________________________________________________________________ f) STATE YOUR CONCLUSION IN CONTEXT OF ________________________________________________________________________________________________________ g) STATE YOUR CONCLUSION IN CONTEXT OF THE CLAIM

On each of the following 1- State the null and alternte hypothesis. 2- Show the test statistic, 3- State the conclusion in terns of the null hypothesis, 4-State the conclusion in terms of the question 5-tell the p-value (if one sided):

Emma dosent believe that women take longer in the restroom than men, so she stands outside the restrooms in the union and times people as they enter and exit. Besides getting strange looks, she collects the following data. The mean time for 30 men was 4 minutes with a standard deviation of 2, while the mean of 20 women was 5 minutes with a standard deviation of 3. Is the mean significantly higher for women than men at a 5% level of significance.

Assume the speed of vehicles along an open stretch of a certain highway in Texas that is not heavily traveled has an approximately Normal distribution with a mean of 71 mph and a standard deviation of 3.125 mph.

1. The current posted speed limit is 65 mph. What is the proportion of vehicles going above the current posted speed limit?
2. What proportion of the vehicles would be going less than 50 mph?
3. What proportion of the vehicles would be going between 60 and 75 mph?  
4. State authorities are cognizant of the road not being heavily trafficked, and that it can handle a higher speed limit. However, they now will implement a high fee for speeding over the new speed limit in order to ensure some level of overall safety. Speeds will be checked by radar. Assume the same Normal distribution of vehicle speeds continues into the future as in the past. What should be the new speed limit such that only about 10% of vehicles will be speeding over the new posted speed limit? Show all of your reasoning/work in answering this.

Using Rcode solve

A company with a large fleet of cars wants to study the gasoline usage. They check the gasoline usage for 50 company trips chosen at random, finding a mean of 25.02 mpg and sample standard deviation is 4.83 mpg.

a. Which kind of confidence interval is appropriate to use here, z-interval or t-interval?

b. What are the assumptions to check for the interval you chose?

c. Please use R to find the critical value the company needs when constructing a (two-sided) 98% CI.

d. Please use R to construct a (two-sided) 98% CI for the mean of the general gasoline usage.

e. Please use R to construct a 98% upper confidence bound for the mean of the general gasoline usage.

f. Create a R function whose argument is the width of CI, and the output is the sample size necessary to achieve such accuracy. The confidence level is fixed at 98%.

g. Apply the function you created in part (f) to demonstrate that larger sample size is required to achieve better accuracy (i.e, narrower CI width). Confidence level is fixed at 98%. Show at least three examples

Write a function called simExp that simulates drawing sample means when lambda=1, with n=10, 30 and 50. Give a histogram for the sample means, as well as the mean and standard deviation of the simulated means. Use 1000 sims. Show that your results are what you would expect theoretically.

A survey of 300 students is selected randomly on a large university campus. They are asked if they use a laptop in class to take notes. Suppose that based on the​ survey, 135 of the 300 students responded​ "yes."

​a) What is the value of the sample proportion p^?

​b) What is the standard error of the sample​ proportion?

​c) Construct an approximate 95 confidence interval for the true proportion p by takingplus or minus 2 SEs from the sample proportion.

Create a crosstab table of frequencies from the data containing case id, age, sex, and marital status, using an Excel pivot table. A crosstab is a table showing the relationship between two or more variables. When the table shows the relationship between two categorical variables, a crosstab is also known as a contingency table or a two-way table. Format the data as number with 1000 separator.

Please outline step by step how to create the pivot table in Microsoft Excel following the criteria above.