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**STAT 3660 Quiz | Complete Solution**

- From Mathematics, Statistics

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1. Multiple Choice: For a confidence interval, as n increases, the margin of error __ __.

(a) stays the same

(b) increases

(c) decreases

(d) may change, however it depends on the data

2. A sample of students were asked to rank their looks compared to the looks of others on a scale from 1 to 10. A 10 means they feel they are more attractive than everyone else while a 1 means they feel they are less attractive than everyone else. The data is below:

7 7 6 7 6 5 7 9 8

10 5 6 8 6 5 8 6 10

5 3 4 8 7 10 7 6 10

The data are summarized below.

Variable n Mean StDev

Rank 27 6.926 1.88

(a) Construct a dotplot of the data.

(b) Estimate the average rank all students would give themselves based on their looks.

(c) Interpret your results from part b. 2

3. Below is a table of class standing for students in my class during a previous semester. Calculate the relative frequencies and add them to the table above.

Class Standing Frequency Relative Frequency

Freshman 9

Sophomore 57

Junior 53

Senior 41

Total 160

4. Below are three histograms. List them in order from smallest to largest standard deviation.

SKIP

5. Multiple Choice: Which of the following is a possible test statistic?

(a) α = 0.05

(b) z = 1.84

(c) p - value = 0.0329

(d) Reject H0 3

6. A study is conducted as to whether there is a relationship between joggers and the consumption of nutritional supplements. A random sample of 210 subjects is selected and they are classified as shown. Test the claim that jogging and consumption of supplements are not related.

Jogging Status Supplements Daily Supplements Weekly Supplements As Needed

Joggers 34 52 23

Non-joggers 18 65 18

The R output is as follows:

> data <- matrix(c(34, 52, 23, 18, 65, 18), byrow=T, nrow=2)

> data

[,1] [,2] [,3]

[1,] 34 52 23

[2,] 18 65 18

> chisq.test(data)

Pearson’s Chi-squared test

data: data

X-squared = 6.6822, p-value = 0.0354

(a) What are the hypotheses for this test?

(b) How many joggers do you expect to take supplements weekly?

(c) How many degrees of freedom does this test have?

(d) What is your conclusion for this test at the 1% significance level? 4

7. In a survey of 1000 women who had given birth, 62% of them had an epidural. I am interested in the proportion of all women who have given birth that had an epidural.

(a) Construct a 90% confidence interval for the proportion of all women who have given birth that had an epidural.

(b) Interpret your confidence interval from (a).

(c) Multiple Choice: An individual claim that 50% of women who have given birth had an epidural. What can you see about the claim?

i. The claim is correct.

ii. The proportion of women who have given birth that had an epidural is not significantly different than 50%.

iii. More than 50% of women who have given birth had an epidural iv. Less than 50% of women who have given birth had an epidural

8. Multiple Choice: Trends in marriage have changed over time. Suppose a researcher would like to know the average age at which a women gets married. He takes a sample of 100 married women. What type of test statistic would you calculate for this test?

(a) Z

(b) t

(c) χ 2

9. Multiple Choice: Suppose a researcher would like to do a perform a test to determine the proportion of individuals with lung cancer that are smokers. A researcher goes to a local hospital and asks 20 lung cancer patients whether or not they are smokers. What type of test statistic would you calculate for this test?

(a) Z

(b) t

(c) χ 2 5

10. Multiple Choice: I would like to know if there is a relationship between whether or not a daughter has ever had breast cancer and whether or not her mother ever had breast cancer. What type of test statistic would you calculate for this test?

(a) Z

(b) t

(c) χ 2

11. According to the National Association of College Stores (NCAS), students spend, on average, $655 on books per year. Suppose the standard deviation for the amount of money students spend on books per year is $240.

(a) What is the probability that a randomly selected student will spend more than $750 on a book in a year?

(b) What is the probability that in a random sample of 35 students, the average amount of money of money they spend on books will be more than $750 on a book in a year?

12. (Multiple Choice) The point of a one mean confidence interval is to find a range of values for which the__ __ __ mean is likely to fall between. (a) sample (b) population

13. A researcher would like to conduct a controlled experiment to test whether or not a new drug will help relieve arthritic pain. To test this, the researcher has 100 participants that are split into two groups. One group will receive the new drug while the other will receive a placebo. The participants do not know whether they are receiving the drug or the placebo, however the researcher, whom will examine them, does. Participants are asked to come in to the research center every week to ask some questions, including some about their pain levels. Circle all the aspects of the study below that make it a good study.

(a) Two groups

(b) Study was double blind

(c) Study was blind

(d) One group received a placebo

(e) Participants were split into two groups but not necessarily randomly

14. For each of the following variables, indicate a type of plot you could use to display it.

(a) Hours slept last night

(b) Method of transportation to campus (walk, drive, etc.)

15. Multiple Choice: Choose the value of the Pearson’s Correlation Coefficient (r) that best describes the two plots.

SKIP

(a) I: -0.821, II: -0.101

(b) I: 0.101, II: 0.821

(c) I: 0.821, II: 0.899

(d) I: 0.821, II: 0.101

(e) I: 0.179, II: 0.101

16. A medical researcher wants to determine if the average hospital stay after a certain procedure is greater than 14 days. The hypotheses for this scenario are as follows: H0 : µ ≤ 14, HA : µ > 14. The researcher randomly samples 28 patients that underwent the procedure and determines their average hospital stay was 15.13 days with a standard deviation of 5.21 days.

(a) What is the test statistic for this test?

(b) What is the p-value of this test?

(c) What is your conclusion for this test?

17. Suppose we would like to find a relationship between the height (X) and shoe size (Y ) of college students. In a survey given one semester, the average height of the students was 67.21 inches with a standard deviation of 4.02 inches. The average shoe size 9.21 with a standard deviation of 1.86. The correlation between the two variables is 0.82.

(a) Multiple Choice: There is a__ __ , __ __ correlation between height and shoe size.

i. positive, strong

ii. positive, moderate

iii. positive, weak

iv. negative, strong

v. negative, moderate

(b) Calculate the regression equation for the data:

(c) Predict the shoe size of an individual who is 65 inches tall.

(d) Calculate the root mean square (RMS) of the data.

**STAT 3660 Quiz | Complete Solution**

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- Submitted On 04 Jul, 2015 01:04:37

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