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.

Imagine you created a new drug that you think will increase IQ. As a responsible researcher, you want to test this drug to see if it does, indeed, significantly alter IQ scores. To that end, you recruit a sample of n=9 individuals and give them the new drug. After one month, you record their IQ scores and find that the mean IQ of the sample is 109. We know that the population distribution of IQ scores has a mean of μ=100 with a standard deviation of σ=15. Use this data to run a full hypothesis test using the z-score hypothesis test to test the hypothesis that people who take your drug have significantly different IQ scores compared to the whole population (alpha of α=0.05, two-tailed test). For your answer to this question, write a paragraph IN YOUR OWN WORDS that contains all of the following information:

Hypotheses

Critical values

Final z-score answer

Conclusion about the null hypothesis

Written summary of the conclusions that can be made from this study

1. When identical parts are being manufactured. They vary from one another. If the variation is normally distributed if:

a) is natural and is to be expected

b) indicates the parts do not meet quality standards

c) indicates an unstable process is developing

2. Probability tells us:

a) how often something actually occurs

b) how often something is expected to occur

c) the number of random samples it takes for an event to occur

3. Unnatural variation is normally the result of:

a) expected variation in the process

b) assignable causes

c) product design choices

4. A histogram is a graph of:

a) the past history of the process

b) machine capability

c) how often events or measurements occur

5. The normal distribution curve:

a) is a picture of how products are distributed from a stable set of conditions

b) provides accurate information about specification limits

c) allows us to identify causes of variation

6. The mean of a sample taken from a population:

a) is written as x

b) is the result of measuring all the individuals

c) determines process capability

7. Range is:

a) the number of times an event occurs

b) the difference between highest and lowest values

c) shown on an x chart

8. The variability of a group is described by:

a) standard deviation

b) population totals

c) the value between the first and last piece produced

9. A “quality” product is one that:

a) is within the specification limits

b) meets the needs and expectations of the customer

c. uses geometric dimensioning and tolerancing

10. Statistical Process Control:

a) tracks the variability of products or services

b) will solve he majority of quality related problems

c) is most useful during 100% inspection

11. The normal distribution of average is:

a) larger than the distribution of individuals

b) narrower than the distribution of individuals

c) the same as the distribution of individuals

12) A product’s key quality characteristics are monitored:

a) during final inspection

b) within +- 0.001

c) using control chart

13. Control limits on an x are:

a) the statistical words for blueprint tolerances

b) based upon the distribution of sample averages

c) used to determine process capability

14) Process capability studies:

a. given information about how a process is behaving

b) are most effective in determining whether or not SPC works

c) require that a single machine be capable of producing at least 2 different parts

15) Values plotted as points on an x chart are:

a) individual values

b) specification limits

c) sample values

16. The pattern of points on an x chart should show a normal distribution that:

a) closely parallels individual measurement

b) shows percent defective

c) is within +- 3 sigma

Angelica Reardon received a 5-year non-subsidized student loan of $15,000 at an annual interest rate of 6.7%. What are Angelica's monthly loan payments for this loan after she graduates in 4 years? (Round your answer to the nearest cent.)

A simple random sample of 10 items resulted in a sample mean of 30. The population standard deviation is σ=20.

a. Compute the 95% confidence interval for the population mean. Round your answers to one decimal place.
( ,  )

b. Assume that the same sample mean was obtained from a sample of 100 items. Provide a 95% confidence interval for the population mean. Round your answers to two decimal places.
( ,  )

Consider a multiple-choice examination with 50 questions. Each question has four possible answers. Assume that a student who has done the homework and attended lectures has a 75% chance of answering any question correctly. (Round your answers to two decimal places.)

(a)

A student must answer 45 or more questions correctly to obtain a grade of A. What percentage of the students who have done their homework and attended lectures will obtain a grade of A on this multiple-choice examination? Use the normal approximation of the binomial distribution to answer this question.

%

(b)

A student who answers 34 to 39 questions correctly will receive a grade of C. What percentage of students who have done their homework and attended lectures will obtain a grade of C on this multiple-choice examination? Use the normal approximation of the binomial distribution to answer this question.

%

(c)

A student must answer 28 or more questions correctly to pass the examination. What percentage of the students who have done their homework and attended lectures will pass the examination? Use the normal approximation of the binomial distribution to answer this question.

%

(d)

Assume that a student has not attended class and has not done the homework for the course. Furthermore, assume that the student will simply guess at the answer to each question. What is the probability that this student will answer 28 or more questions correctly and pass the examination? Use the normal approximation of the binomial distribution to answer this question.