Math 11 Advanced Stats Test

Name__________________

Choose the best answer for each by writing your answer in the space provided.

/30

(8 pts)

___ 1. The Nova Scotia Department of Health wishes to examine smoking rates amongst teenage females in HRM. It decides to take samples from a number of the high schools in the city. It was determined that the number of people surveyed would be as follows: 100 students from Citadel High 85 students from Dartmouth High

140 students from Halifax West 70 students from J.L Ilsley

95 students from Lockview High

This sampling method is an example of: a. cluster sample ___ 2.

b. stratified random sample

c. simple random sample

d. systematic sample

The sample mean is:

a. a fixed value c. an interval estimator

b. always equal to the population mean d. a point estimate

___ 3. The confidence interval of 22 to 28 is determined from a set of data. What is the margin of error? a. 6

b. 3

c. 25

d. 50

___ 4. A sample of Citadel High students were chosen at random. Students were asked how many hours of sleep they get on a normal weeknight. What is the confidence level for the survey? The results were reported as follows:

“The average Citadel student gets 6.9 hours of sleep. These results are accurate within 1.3 hours, 19 times out of 20.” a. 0%

b. 90%

c. 95%

d. 99%

Samples from three brands of batteries A, B, & C were tested for voltage and their graphs are shown below. Use this graph to answer questions 5 and 6.

___ 5. Which brand has the greatest standard deviation? a. Brand C

b. Brand B

c. Brand A

d. not enough information

c. Brand C

d. not enough information

___ 6. Which brand do you think is more reliable? a. Brand B

b. Brand A

___ 7. Which of the following set of numbers has the lowest standard deviation? A. {0, 4, 8, 12, 16}

B. {1, 2, 3, 4, 5, 6}

C. {0, 40, 80, 120, 160}

D. {1000, 1000, 1000, 1000,1000}

___ 8. A random sample of Doritos potato chips were selected from a grocery store’s inventory and weighed. Doritos claims that each bag should contain 65g of chips. Here are the weights in grams for 15 bags of chips. 62.14 64.21 66.01 A) B) C) D) E)

63.20 63.78 65.01

65.31 65.81 63.59

61.94 62.91 63.71

64.75 62.73 64.20

The standard deviation for this sample is 1.214 The median mass of a bag of Doritos is 63.95 g 95 % of the bags of Doritos are between 62 and 66 grams The range for this data is 4.07 grams The median life expectancy for an enemy soldier in a Chuck Norris film: 31 seconds

Given the above data, which of the above statements is NOT incorrect? a. B

b. C

Part B: Constructed Response

c. D

d. A (22 points)

1. The time, in seconds, that students take from the beginning of class to check their phone for a text message is shown below: (4 pts) 114 117 119 120 120 120 122 122 123 130 a) Find the mean time. _______ b) Complete the table and calculate standard deviation.

xi

(xi – x) deviation

(xi – x)2 deviation2

c) Are any of the data points from the above sample outliers? Explain how you know.

Sum 2. An investigator interested in finger-tapping behavior conducts the following study: Students are asked to tap as fast as they can with their ring finger. The hand is cupped and all fingers except the one being tapped are placed on the surface. Either the right or the left hand is used, at the preference of the student. At the end of 15 seconds, the number of taps for each student is recorded. The histogram is presented below. (1 pt) 10 9 8 7 6 5 4 3 2 1 0

frequency

number of taps 25

35

45

55

65

75

a) How many students are in the study? ______________________________ b) What percentage of students had fewer than 45 taps in 15 seconds? _______________ 3. The length of time required to process an order at the MacDonald’s drive-thru on Quinpool Road is normally distributed with a mean of 3.5 minutes and a standard deviation of 0.8 minutes. (3 pts) a) Label the horizontal axis with the appropriate values. b) Approximately what percentage of the times will fall between 2.7 and 5.9 minutes? _____________

50 60 52

A population of adult female white-tailed deer has a mean of 55kg and a standard deviation of 4.2kg. A random sample of 30 deer is selected and each mass (kg) is recorded as shown: (2 pts) 58 62 45 52 56 58 41 57 56 51 55 56 55 58 53 54 60 59 55 52 58 47 53 56 59 52 58

a.

Determine the sample mean of the masses. _________________

b.

What is the population standard deviation? _________________

c.

If samples of 30 deer were repeatedly collected form this population, what would be the value of the standard deviation of the sample means?

5.

Samples of the same size number of the number of minutes of exercise that teenagers get in a day are repeatedly collected from a known population ( µ = 67; σ = 8.06 ). A sampling

4.

distribution of the sample means is constructed. It is determined that the mean of the sampling distribution of x is 67, while the standard deviation of the sampling distribution of x is 2.50. (2.5 pts) a. Describe the shape of this sampling distribution.

b. Explain why the means are equal.

c. Explain why the standard deviations are different.

6. The supplier of calculator batteries advertises that the mean life of their AAA batteries is 400 hours with a standard deviation of 15 hours. The number of hours of classroom use is recorded for a randomly selected sample of 30 batteries. (3 pts) 423 392 399

369 408 371

387 377 377

407 401 390

393 363 396

394 391 372

371 385 410

377 382 399

389 400 386

379 381 390

a) Determine a point estimate for this sample. _____________________________ b) Determine the 90% confidence interval.

c) Based on your calculations, is it appropriate to write a letter of complaint to the company suggesting that their advertisement is not accurate.

7. It is estimated that Peninsular Halifax’s population is approximately 60 000 people. A survey of 1300 people was conducted and found that, on average, only 65% of Peninsular Halifax’s residents use snow tires on their vehicles. (3.5 pts) a) Is this approximately a binomial experiment? Explain how you would know.

b) Give the 95% confidence interval for this sample.

c) What is the margin of error? _____________________ d) How would the confidence interval change if you were dealing with a 90% confidence interval? (You do not have to calculate this interval)

8. On Monday, the Social Committee of Student Council surveyed the entire Citadel High student population to find out what format appeals to students in an effort to make school dances more successful. This is a time-consuming method of getting information. You suggest that a reliable result could have been achieved by sampling about 70 students. Consider the following options: (3 pts) i) Two representatives of the Social Committee stand at the door of the dance tonight and select students to answer the questionnaire. ii) During announcements, students are invited to come to the office to complete a questionnaire. a) Identify the type of sampling in each of the options above and explain why each is not likely to give reliable results.

b) Describe how you would use one of cluster, stratified or systematic sampling (do not use simple random sampling!!) to create your sample. You only have to describe one possible sampling method. (remember: sample about 70 students)