Deck 28: Inference for Decision Making

Question 1

A truck company wants on-time delivery for 98% of the parts they order from a
Metal manufacturing plant. They have been ordering from Hudson Manufacturing
But will switch to a new, cheaper manufacturer (Steel-R-Us) unless there is
Evidence that this new manufacturer cannot meet the 98% on-time goal. As a test
The truck company purchases a random sample of metal parts from Steel-R-Us,
And then determines if these parts were delivered on-time. Which hypotheses
Should they test?

Answer 1

C

Question 2

Which of the following is not an assumption or condition that needs to be checked
For a two-sample t-test for the difference between two means?

A) Independent Groups
B) Randomization
C) 10% Condition
D) Nearly Normal Condition
E) All of the above must be checked.

Answer 2

E

Question 3

A manufacturer of cordless electric shavers sampled 13 from a day's production
And found the mean time of continuous usage without recharging to be 410 minutes with a sample standard deviation of 30 minutes. We can assume that times are normally
Distributed. We wish to test if the true mean operating time without recharging is more
Than 400 minutes. The correct null and alternative hypotheses are

Answer 3

B

Question 4

A newspaper poll asked respondents if they trusted "eco friendly" labels on
Cleaning products. Out of 1000 adults surveyed, 498 responded "yes." We would like to
Test if the proportion of respondents that trust these labels is at least 50%. The calculated
Test statistic value is

A) -.126
B) -2.45
C) 1.27
D) -1.89
E) .139

Question 5

We have calculated a 95% confidence interval and would like our next
Confidence interval to have a smaller margin of error without losing any
Confidence. In order to do this, we can I. change the $z ^ { * }$ value to a smaller number.
II. take a larger sample.
III. take a smaller sample.

A) I only
B) II only
C) III only
D) I and II
E) I and III

Question 6

A newspaper poll asked respondents if they trusted "eco friendly" labels on
Cleaning products. Out of 1000 adults surveyed, 498 responded "yes." We would like to
Test if the proportion of respondents that trust these labels is at least 50%. The correct
Alternative hypothesis is
Chapter 13: Calculate the appropriate test statistic.

Question 7

A human resources manager at a large company wants to estimate the proportion
Of employees that would be interested in reimbursement for college courses. If she
Wishes to be 95% confident that her estimate is within 5% of the true proportion, how
Many employees would need to be sampled?

A) 271
B) 385
C) 543
D) 646
E) 1234

Question 8

During economic downturns, companies attempt to downsize their workforces by
Offering early retirement incentives to older employees. A survey of 723 companies
Found that 195 engage in such downsizing practices. The estimated proportion of
Companies that downsize their workforces by offering early retirement incentives is

A) .50
B) .73
C) 195
D) .27
E) .67

Question 9

A manufacturer of cordless electric shavers sampled 13 from a day's production
And found the mean time of continuous usage without recharging to be 410 minutes with a sample standard deviation of 30 minutes. We can assume that times are normally
Distributed. We wish to test if the true mean operating time without recharging is more
Than 400 minutes. The correct calculated value of the test statistic is

A) 1.20
B) -0.333
C) -2.52
D) -1.20
E) 2.79

Question 10

A P-value indicates

A) the probability that the null hypothesis is true.
B) the probability that the alternative hypothesis is true.
C) the probability of the observed statistic given that the null hypothesis is true.
D) the probability of the observed statistic given that the alternative hypothesis is true.
E) None of the above.

Question 11

A local politician was interested in determining whether income level affects
Opinion regarding the government's bailout bill for easing the 2008 financial crisis on
Wall Street. He surveyed a sample of his constituents and got the following results. The
Calculated value of the Chi Square statistic is $$\begin{array}{l}\text { \quad\quad\quad\quad\quad\quad\quad\quad\quad\quad \quad Opinion }\\\begin{array} { | l | c | c | } \hline { \text { Income Level } } & \text { Favor } & \text { Oppose } \\\hline > \$ 200,000 & 38 & 29 \\\hline \$ 50,000 \text { to } \$ 200,000 & 30 & 42 \\\hline < \$ 50,000 & 32 & 59 \\\hline\end{array}\end{array}$$

A) 7.433
B) 29.13
C) 40.70
D) 5.999
E) 2.347

Question 12

A type I error is committed when

A) we don't reject a null hypothesis that is true.
B) we reject a null hypothesis that is false.
C) we reject a null hypothesis that is true.
D) we don't reject a null hypothesis that is false.
E) none of the above

Question 13

After computing a confidence interval, the investigator believes that the results
Are meaningless because the width of the interval is too large. In reconstructing the
Interval, the investigator should

A) decrease the sample size
B) increase the level of confidence
C) increase the sample size
D) reduce the population variance
E) none of the above

Question 14

The weights of soy patties sold by Veggie Burgers Delight are normally
Distributed. A random sample of 15 patties yields a mean weight of 3.8 ounces with a
Sample standard deviation of 0.5 ounces. At the .05 level of significance, perform a
Hypothesis test to see if the true mean weight is less than 4 ounces.
The correct null and alternative hypotheses are
Chapter 13: Calculate the appropriate test statistic.

Question 15

Which is true about a 99% confidence interval based on a given sample?
I) The interval contains 99% of the population.
II) Results from 99% of all samples will lie in this interval.
III) The interval is wider than a 95% confidence interval would be.

A) None
B) I only
C) II only
D) III only
E) I and III

Question 16

A contact lens wearer read that the producer of a new contact lens boasts that their
Lenses are cheaper than contact lenses from another popular company. The null hypothesis $H _ { 0 } : \mu _ { \text {old } } - \mu _ { \text {new } } = 0$ is tested against the alternative $H _ { A } : \mu _ { \text {old } } - \mu _ { \text {new } } > 0$ . Which of the following would be a Type II error?

A) Deciding that the new lenses are cheaper, when in fact they really are.
B) Deciding that the new lenses are cheaper, when in fact they are not.
C) Deciding that the new lenses are not really cheaper, when in fact they are.
D) Deciding that the new lenses are not really cheaper, when in fact they are not.
E) It does not matter.

Question 17

A local politician was interested in determining whether income level affects
Opinion regarding the government's bailout bill for easing the 2008 financial crisis on
Wall Street. He surveyed a sample of his constituents and got the following results. The
Correct null hypothesis to be tested is $$\begin{array}{l}\text { \quad\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad Opinion }\\\begin{array} { | l | c | c | } \hline { \text { Income Level } } & \text { Favor } & \text { Oppose } \\\hline > \$ 200,000 & 38 & 29 \\\hline \$ 50,000 \text { to } \$ 200,000 & 30 & 42 \\\hline < \$ 50,000 & 32 & 59 \\\hline\end{array}\end{array}$$

A) There is no relationship between income level and opinion.
B) There is a relationship between income level and opinion.
C) Opinion and income level are independent.
D) Both A and C
E) Both B and C

Question 18

In economic downturns, companies attempt to downsize their workforces by
Offering early retirement incentives to older employees. A survey of 723 companies
Found that 195 engage in such downsizing practices. The 99% confidence interval for the
Proportion of companies that downsize their workforces by offering early retirement
Incentives is

A) .19 to .35
B) .65 to .81
C) .19 to .47
D) .69 to .77
E) .23 to .31

Question 19

Suppose that a manufacturer is testing one of its machines to make sure that the
Machine is producing more than 97% good parts

Question 20

We have created a 95% confidence interval for µ with the result (10, 15). What
Conclusion will we make if we test $$H _ { 0 } : \mu = 16 \text { versus } H _ { A } : \mu \neq 16 \text { at } \alpha = .05 ?$$

A) Reject the null hypothesis
B) Accept the null hypothesis
C) Fail to reject the null hypothesis.
D) Reject the alternative hypothesis.
E) No decision can made from the information given.

Question 21

Chris Columbus is responsible for controlling inventory levels for four types of
Sailboats sold by his company. Chris takes a sample of 48 boats sold over the past
Several months to determine if demand is the same for each type. His results are as
Follows: $$\begin{array} { l l } \text { Type of Boat } & \text { Sales } \\\text { Pirate's Revenge } & 15 \\\text { Jolly Roger } & 11 \\\text { Sails Delight } & 10 \\\text { Cruiser Cove } & 12\end{array}$$
The calculated value of the Chi Square statistic is

A) 7.815
B) 1.17
C) 22.35
D) -1.17
E) 12.56

Question 22

Absorption rates into the body are important considerations when manufacturing a generic version of a brand-name drug. A pharmacist read that the absorption rate into the body of a new generic drug $( \mathrm { G } )$ is the same as its brand-name counterpart (B). She has a researcher friend of hers run a small experiment to test
$H _ { 0 } : \mu _ { G } - \mu _ { B } = 0$ against the alternative $H _ { A } : \mu _ { G } - \mu _ { B } \neq 0$ . Which of the following would be a Type I error?

A) Deciding that the absorption rates are the same, when in fact they are.
B) Deciding that the absorption rates are different, when in fact they are.
C) Deciding that the absorption rates are the same, when in fact they are not.
D) Deciding that the absorption rates are different, when in fact they are not.
E) The researcher cannot make a Type I error, since he has run an experiment.

Question 23

Which of the following is not an assumption or condition that needs to be checked
For a paired t-interval?

A) Paired Data
B) Independent Groups
C) Randomization
D) 10% Condition
E) Nearly Normal Condition

Question 24

The weights of soy patties sold by Veggie Burgers Delight are normally
Distributed. A random sample of 15 patties yields a mean weight of 3.8 ounces with a
Sample standard deviation of 0.5 ounces. At the .05 level of significance, perform a
Hypothesis test to see if the true mean weight is less than 4 ounces.
The correct calculated value of the test statistic is

A) -0.4
B) 0.4
C) -1.55
D) 1.55
E) 2.79

Question 25

A professor was interested in determining whether the prices of new textbooks in
The bookstore were higher than if purchased online. She selected 6 textbooks and priced
Each at the bookstore and online.
Paired T-Test and CI: Bookstore, Online Paired $\mathrm{T}$ for Bookstore - online

$\begin{array}{lrrrr} & \text { N } & \text { Mean } & \text { StDev } & \text { SE Mean } \\ \text { Bookstore } & 6 & 115.00 & 22.36 & 9.13 \\ \text { Online } & 6 & 105.83 & 13.20 & 5.39 \\ \text { Difference } & 6 & 9.17 & 13.20 & 5.39\end{array}$

95\% lower bound for mean difference: -1.69
T-Test of mean difference $=0(\mathrm{vs}>0): \mathrm{T}$ -Value $=1.70 \quad$ P-Value $=0.075$

Based on her analysis, we can conclude at the .05 level of significance that

A) The prices are the same in the bookstore and online.
B) The prices are higher in the bookstore.
C) The prices are higher online.
D) The prices are different in the bookstore and online.
E) The analysis is not conclusive.