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Math 140 Final Exam Spring 2016 Name:

Instructor:

Days and Time of Class:

INSTRUCTIONS

• Show all work, including calculator commands that you use. • Write your final answer in the ANSWER box, if one is provided. • Please write in pencil and erase anything that you don’t want graded. • Graphing calculators are allowed only if nothing has been stored in them. • Please return the formula sheet with your exam. • Please raise your hand when finished and pack up after your exam has been collected. • No cell phones may be turned on or in sight at any time during the exam. If your phone is visible during

the exam, your papers will be collected and you will receive an F on the exam.

Problem Possible Points Points Scored

1 3

2 4

3 3

4 4

5 5

6 4

7 17

8 9

9 12

10 14

11 12

12 9

13 4

TOTAL 100

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1. In 2014, out of the 21,521,739 women aged 15–24 in the United States, 990 committed suicide. What was the suicide rate per 100,000 women this age? (Round your answer to one decimal place.)

2. Among a group of 12 friends, the average salary is $93,167 with a standard deviation of $207,465. The median salary is $29,500 with an interquartile range of $25,000. One of the friends has a salary of $750,000.

a. (Fill in the blank.) Half of the friends have a salary that is less than .

b. If the salary of $750,000 is removed from the data set, which of the following should decrease quite a bit? (Circle all that apply.)

MEAN MEDIAN STANDARD DEVIATION INTERQUARTILE RANGE

3. Circle the best interpretation of the standard deviation.

A. It is the difference between the third quartile and the first quartile.

B. It gives a typical distance between each value and the mean.

C. It is roughly equal to the largest number minus the smallest number.

D. It is the distance from the mean to the largest or smallest value, whichever is greater.

4. The following scores have a mean of 69 and a standard deviation of 19.7.

46 57 63 88 91

Which score contributes the most to the standard deviation? __________

Circle the best reason. A. It is the largest number. B. It is the smallest number. C. It is farthest from the mean. D. It is closest to the mean.

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5. A student at Sacramento State University asked hundreds of other students how many minutes of exercise they get in a typical day. The results are summarized in this histogram.

a. How many students exercise between 20 minutes and 40 minutes a day?

b. What is the shape of this distribution? (Circle one.)

SKEWED RIGHT SKEWED LEFT NORMAL SYMMETRIC

6. Recently, 2,780 students graduated from CSUN with bachelor’s degrees in psychology. CSUN wants to estimate their yearly salary and is able to find 1,892 of these graduates, who report an average salary of $33,665. Suppose that if CSUN had found all 2,780 graduates, they would have reported an average salary of $31,549. Match the following.

Population A. 1,892 Population size B. 2,780 Parameter, 𝜇 C. $31,549 Sample D. $33,665 Sample size, n E. all recent CSUN psychology graduates Statistic, 𝑥 F. the recent CSUN psychology graduates found by CSUN

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7. Nate predicted that more than 80% of teens check their phones hourly. A survey published last week of 1,200 randomly-selected teens found that 82.5% of them check their phones hourly. Does this survey provide statistically significant evidence in favor of Nate’s hypothesis?

a. Write the hypotheses: Ho: Ha:

You should have used a symbol in your hypotheses. What does it stand for? (Circle one.)

A. the proportion of all teens who check their phones hourly

B. the proportion of all teens in the sample of 1,200 who check their phones hourly

C. the number of teens who check their phones hourly

D. the number of all teens in the sample of 1200 who check their phones hourly

b. Assume that the null hypothesis is true.

• What is the mean of the sampling distribution of the sample proportion?

• What is the standard error of the sampling distribution? Round to two decimal places.

• Still assuming that the null hypothesis is true, complete this sketch of the sampling distribution of the sample proportion.

• Mark the result from the sample on it and shade in the area that represents the p-value.

c. In this conclusion, circle the right words in each pair. Use a significance level of α = .05.

• The result from the survey IS / IS NOT consistent with a population percentage of 80%.

• There IS / IS NOT statistically significant evidence in favor of Nate’s hypothesis that the percentage of teens who check their phones hourly is more than 80%.

• If we could ask all teens, it IS / IS NOT plausible that the percentage who check their cell phones hourly is 80%.

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8. In 2010, total scores on the three parts of the SAT exam followed a Normal distribution, with mean 1509 and standard deviation 312. (For each part, you must include your calculator command and round your answer to four decimal places.)

a. What proportion of scores were below 1000? Label the sketch and shade the appropriate area.

b. How many standard deviations is a score of 1000 from the mean?

c. What score did a student need to be in the 90th percentile? Label the sketch and shade the appropriate area.

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9. CSUN is testing a new on-line course. The list below shows the number of days needed for a random sample of 10 CSUN students to complete the course.

52 59 54 42 44 40 42 48 55 54

a. Assuming that the distribution of days needed to complete the course is approximately Normal, find a 95% confidence interval for the mean number of days to complete the course. (Round your answers to three decimal places, as necessary.)

b. Circle the best way to complete the following conclusion:

We are 95% confident that the mean number of days

A. it took these 10 students to complete the course is in this interval.

B. it would take all CSUN students to complete the course is in this interval.

C. it would take a different random sample of 10 CSUN students to complete the course is in this interval.

c. Can you reject the hypothesis that the mean number of days to complete the course for all CSUN students is 50 days? (Circle one)

A. No. Because 50 days is in the interval, it is plausible the mean is 50 days.

B. No. Because 50 days is not in the interval, it is not plausible the mean is 50 days.

C. Yes. Because 50 days is in the interval, it is plausible the mean is 50 days.

D. Yes. Because 50 days is not in the interval, it is not plausible the mean is 50 days.

d. Write your interval in the form observed value ± margin of error.

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10. Consumer Reports magazine conducted a survey to obtain customer satisfaction ratings for large retail stores. Each response was summarized by an overall satisfaction score between 0 and 100, with 100 representing complete satisfaction.

A random sample of 25 shoppers visited Target, and their mean satisfaction rating was 79, with a standard deviation of 12. A random sample of 30 shoppers visited Walmart, and their mean satisfaction rating was 71, with a standard deviation of 16.

Conduct a hypothesis test to determine if there is a difference in the mean satisfaction ratings for all shoppers at Target and Walmart.

a. Write the hypotheses on the lines below. Let µ1 represent the mean satisfaction score for Target, and µ2 represent the mean score at Walmart.

Ho: Ha:

b. Use your calculator to compute the test statistic t and the p-value, rounding each to four decimal places.

t = ______________ p-value = __________________

c. Here is the sampling distribution of x1 – x2( ) , assuming H0 is true. The differences have a

standard error of SEest ≈ 3.8.

• Label each of the marked locations along the axis.

• Compute and then mark the location of

the sample difference x1 – x2( ) .

• Shade the region that gives the p-value.

d. Circle the best conclusion below. Use a significance level of α = .05.

A. Reject H0. There is statistically significant evidence of a difference in mean customer satisfaction at Target and Walmart.

B. Reject H0. There is no statistically significant evidence for a difference in mean customer satisfaction at Target and Walmart.

C. Do not reject H0. There is statistically significant evidence of a difference in mean customer satisfaction at Target and Walmart.

D. Do not reject H0. There is no statistically significant evidence for a difference in mean customer satisfaction at Target and Walmart.

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11. We suspect that some age groups are more likely to use a cell phone as their main phone than are other age groups. Do data confirm this claim? Below is a two-way table that categorizes a random sample by age group and by which type of phone they mainly use.

Age (years) Landline Mainly Cell Phone Mainly Total 18–29 154 46 200 30–49 265 70 335 50–64 185 45 230 65 or Older 152 35 187 Total 756 196 952

a. Which is larger, the proportion of 18–29 year olds who mainly use a cell phone or the proportion of 30–49 year olds who mainly use a cell phone?

After filling in the blank above, circle the best reason for your answer.

A. 70 is larger than 46

B. 335 is larger than 200

C. 46/200 is larger than 70/335

D. 70/196 is larger than 46/196

b. Assuming that the two variables, Age and Phone Type, are independent, calculate the expected count of the people in this sample who are in the 18–29 age category and rely mainly on cell phones. Show the formula you used for this calculation and the details of your work. (Round to four decimal places.)

c. (Circle one of the capitalized words in each pair.) In this context, “independent" means that the proportion of people who rely mainly on landlines is EQUAL / DIFFERENT for all age groups and the proportion of people who rely mainly on cell phones is EQUAL / DIFFERENT for all age groups.

d. Here are the results of a chi-square test of the null hypothesis that the two variables, Age and Phone Type, are independent.

Statistic DF Value p--value 𝜒! 3 1.2788 0.7342

Circle the correct words in each capitalized pair below to provide an appropriate conclusion for this test.

• Because the p-value is so large, we REJECT / FAIL TO REJECT the null hypothesis.

• We CAN / CANNOT conclude that the variables, Age and Phone Type, are associated.

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12. This scatterplot shows the unemployment rate, as a percent, for people with various numbers of years of education. For example, 12 years of education represents a high school degree. The regression equation is

Unemployment Rate = 12.3 − 0.55 Years of Education

a. Use the equation to estimate the unemployment rate for someone with 15 years of education.

b. Here is the scatterplot with the regression line. Circle the best estimate of the correlation coefficient:

–.90

–.50

–.10

0

.50

.90

c. Complete this interpretation of the slope of the regression line by filling in the blanks and circling INCREASE or DECREASE.

For each additional , the

tends to INCREASE / DECREASE by .

13. Fertility rate is the average number of children per woman. A study last month in Korea found that “the correlation coefficient between housing prices and total fertility rate was –0.070.” Circle the best word in each group to complete these interpretations of this result.

• The higher the cost of housing, the FEWER / MORE children women tend to have.

• The relationship between the cost of housing and the average number of children per woman is STRONG / MODERATE / WEAK.

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SCRATCH WORK CAN GO ON THIS PAGE (WON’T BE GRADED)

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Math 140 Formulas

sample mean: x =x∑

n

sample standard deviation: s =(x − x )2∑n −1

z-score: z = x − xs

interquartile range: IQR = Q3 – Q1

standard error of sampling distribution of p̂ : SE =p 1− p( )

n

standard error of sampling distribution of x : SE = σn

general confidence interval: observed value ± margin of error

confidence interval for p: p̂ ± m where m = z*⋅ p̂ 1− p̂( )

n

confidence interval for µ : x ± m where m = t * sn

general test statistic:

observed value− hypothesized valueSE

one-proportion z-test statistic: z = p̂ − p0

SE where SE =

p0 1− p0( )n

two proportion z-test statistic: z =p̂1 − p̂2( )− 0

SE

where SE = p̂ 1− p̂( ) 1n1

+ 1n2

⎛⎝⎜

⎞⎠⎟

and p̂ = number of successes in both samplesn1 + n2

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t-test statistic for a mean: t = x − µSEEST

where SEEST =sn

two sample t-test statistic: t =x1 – x2( )− 0SEEST

where SEEST =s12

n1+s22

n2

chi-square statistic: χ 2 =O − E( )E

2

∑ where E =

row total( ) ⋅ column total( )grand total( )

correlation: r =1

n −1x − xsx

⎛⎝⎜

⎞⎠⎟

y − ysy

⎛

⎝⎜⎞

⎠⎟∑ =

1n −1

zx ⋅ zy∑

regression equation: predicted = a + bx

regression coefficients: b = r

sysy

a = y − bx

Calculator Commands

normalcdf(lower,upper,µ,σ )

invNorm(area,µ,σ )