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# MCQs: Statistics 2

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The marketing manager of a large supermarket chain would like to use shelf space to predict the sales of pet food. For a random sample of 12 similar stores, she gathered the following information regarding the shelf space, in feet, devoted to pet food and the weekly sales in hundreds of dollars.

Store 1 2 3 4 5 6
Shelf Space 5 5 5 10 10 10
Weekly Sales 1.6 2.2 1.4 1.9 2.4 2.6

Store 7 8 9 10 11 12
Shelf Space 15 15 15 20 20 20
Weekly Sales 2.3 2.7 2.8 2.6 2.9 3.1

What is the estimated regression equation?

A.f\$hat{y}f\$ = 1.45 + 0.074x
B.f\$hat{y}f\$ = 2.63 + 0.724x
C.f\$hat{y}f\$ = 1.45 + 0.724x
D.f\$hat{y}f\$ = 2.63 - 0.174x

Outliers are observations that
A.lie outside the sample
B.render the study useless
C.lie outside the typical pattern of points
D.disrupt the entire linear trend

Multiple myeloma or blood plasma cancer is characterized by increased blood vessel formulation in the bone marrow that is a prognostic factor in survival. One treatment approach used for multiple myeloma is stem cell transplantation with the patient's own stem cells. The following data represent the bone marrow microvessel density for a sample of 7 patients who had a complete response to a stem cell transplant as measured by blood and urine tests. Two measurements were taken: the first immediately prior to the stem cell transplant, and the second at the time of the complete response.

Patient 1 2 3 4 5 6 7
Before 158 189 202 353 416 426 441
After 284 214 101 227 290 176 290

At the .01 level of significance, is there sufficient evidence to conclude that the mean bone marrow microvessel density is higher before the stem cell transplant than after the stem cell transplant?
A.No
B.Yes
C.Cannot Determine

A pharmaceutical company is testing the effectiveness of a new drug for lowering cholesterol. As part of this trial, they wish to determine whether there is a difference between the effectiveness for women and for men. Assume α = 0.05. What is the test value? Women Men
Sample size 50 80
Mean effect 7 6.95
Sample variance 3 4

A.t = 3.252
B.z = 0.081
C.t = 0.151
D.z = 0.455

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#### Solution Summary

The solution provides answers to multiple choice questions. Relevant workings are provided in the excel spreadsheet.

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## Statistics Practice questions: Confidence interval, hypotheses, probability, distribution

See attached file for graphs and tables.

1. A study of 45 bolts of carpet showed that their average length was 78.2 yards. The standard deviation of the population is 1.6 yard.Which of the following is the 95% confidence interval for the mean length per bolt of carpet?

A 77.8 < µ< 78.6
B 77.3 < µ< 79.1
C 78.0 < µ< 78.4
D 77.7 < µ< 78.7

2. For the conjecture "The average weight of a cuckoo bird is less than \$2.5 pounds", the null and alternative hypotheses are:

A) H0 : The average weight of a cuckoo bird is less than or equal to \$2.5 pounds. H1: The average weight of a cuckoo bird is less than \$2.5 pounds.
B) H0: The average weight of a cuckoo bird is equal to \$2.5 pounds. H1: The average weight of a cuckoo bird is less than \$2.5 pounds.
C) H0: The average weight of a cuckoo bird is more than \$2.5 pounds. H1: The average weight of a cuckoo bird is less than \$2.5 pounds.
D) H0: The average weight of a cuckoo bird is less than \$2.5 pounds. H1: The average weight of a cuckoo bird is more than or equal to \$2.5 pounds.

3. Find the probability P (z > 0.73) using the standard normal distribution.

A) 0.2673 B) 0.7673 C) 0.7327 D) 0.2327

4. If a normally distributed group of test scores have a mean of 70 and a standard deviation of 12, find the percentage of scores that will fall below 50.

A) 4.75% B) 45.25% C) 6.75% D) 35.54%

5. The average hourly wage of workers at a fast food restaurant is \$6.50/hr. Assume the wages are normally distributed with a standard deviation of \$0.45. If a worker at this fast food restaurant is selected at random, what is the probability that the worker earns more than \$6.75?

A) 28.8% B) 27.6% C) 42.1% D) 5.2%

An apartment building has the following distribution of apartments:
1 bedroom 2 bedroom 3 bedroom
1st floor 3 1 1
2nd floor 2 2 2
3rd floor 1 4 1

If an apartment is selected at random, what is the probability that it is on the 2nd floor or has 2 bedrooms?

a) 7 b) 6 c) 13 D) 11
11 11 17 17

Box A contains the numbers 1, 2, 3, and 4. Box B contains the numbers 5, 6, 7, and 8. A number is first drawn from Box A and then another number from Box B. Using the figure below, how many outcomes are possible if both numbers are even?

A) 16 b) 4 C) 6 d) 8

A University has 10,000 students of which 35% are male and 65% are female. If a class of 30 students is chosen at random from the university population, find the mean and variance of the number of male students.

A) Mean = 19.5, Variance = 2.6
C) Mean = 19.5, Variance = 6.8
B) Mean = 10.5, Variance = 2.6
D) Mean = 10.5, Variance = 6.8

The figure below is an example of a negatively skewed distribution

True or false (refer to figure above)?

Find the probability P (z < 0. 17) using the standard normal distribution. A) 0.8300 B) 0.4325 C) 0.5675 D) 0.0675
The staff at a small company includes: 4 secretaries, 20 technicians, 4 engineers, 2 executives, and 50 factory workers. If a person is selected at random, what is the probability that he or she is a factory worker?

A) 1 B) 1 C) 5 D 2
4 8 8 5

In a second grade class containing 15 girls and 11 boys, 2 students are selected at random to give out the math papers. What is the probability that both are girls?

A) 15. 15 B) 15 . 14 C) 15 . 3
26 26 26 25 26 5

D) 11 . 2
26 5

A Coin is tossed 5 times. Find the probability that all 5 tosses are tails

A) 1 B) 1 C) 1 D) 1
5 25 10 32

Find the area under the standard normal distribution curve between z =0 and z = &#8722;2.16.

A) -2.1600 B) 0.9846 C) 0.4846 D) 0.3708

Which of the following is the properly rounded mean for the given data?
7, 8, 13, 9, 10, 11

A) 10 B) 9.7 C) 9.67 D) 9
If a set of data has 49 values with a variance of 9.6, then the standard deviation is .
A) 1.4 B) 0.4 C) 0.2 D) 3.1
If a data set has 9 values and a standard deviation 9.4, then the variance is .
A) 88.4 B) 3.1 C) 29.5 D) 28.2

The staff at a small company includes: 4 secretaries, 20 technicians, 4 engineers, 2 executives, and 50 factory workers. If a person is selected at random, what is the probability that he or she is a factory worker?

A) 1 B) 1 C) 5 D) 2
4 8 8 5

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