Deck 15: Testing Hypotheses

Question 1

A pharmaceutical company wants to answer the question whether it takes longer than 45 seconds for a drug in pill form to dissolve in the gastric juices of the stomach.A sample was taken from patients taken the given drug in pill form and times for the pills to be dissolved were measured.State assumptions of the test.
I.The subjects must be part of a medical study group investigating the drug.
II.The subjects in the sample must be randomly selected from a population.
III.The sample data must come from a normally distributed population of observations for
The variable under study.

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

Answer 1

II and III

Question 2

A pharmaceutical company wants to answer the question whether it takes longer than 45 seconds for a drug in pill form to dissolve in the gastric juices of the stomach.A sample was taken from patients taken the given drug in pill form and times for the pills to be dissolved were measured.State the hypotheses to test this question.

A) $H _ { 0 } : \mu = 45 \mathrm { sec } ; H _ { A } : \mu \leq 45 \mathrm { sec }$
B) $H _ { 0 } : \mu < 45 \mathrm { sec } ; H _ { A } : \mu = 45 \mathrm { sec }$
C) $H _ { 0 } : \mu = 45 \mathrm { sec } ; H _ { A } : \mu > 45 \mathrm { sec }$
D) $H _ { 0 } : \mu \geq 45 \mathrm { sec } ; H _ { A } : \mu < 45 \mathrm { sec }$
E) $H _ { 0 } : \mu > 45 \mathrm { sec } ; H _ { A } : \mu \leq 45 \mathrm { sec }$

Answer 2

$H _ { 0 } : \mu = 45 \mathrm { sec } ; H _ { A } : \mu > 45 \mathrm { sec }$

Question 3

A skeptical paranormal researcher claims that the proportion of Americans that have seen a UFO is less than 5%.

A) $H _ { 0 } : p < 0.05 , H _ { A } : p = 0.05$
B) $H _ { 0 } : p = 0.05 , H _ { A } : p > 0.05$
C) $H _ { 0 } : p > 0.05 , H _ { A } : p = 0.05$
D) $H _ { 0 } : p = 0.05 , H _ { A } : p < 0.05$
E) $H _ { 0 } : p < 0.05 , H _ { A } : p > 0.05$

Answer 3

$H _ { 0 } : p = 0.05 , H _ { A } : p < 0.05$

Question 4

In the past, the mean running time for a certain type of flashlight battery has been 8.5 hours.
The manufacturer has introduced a change in the production method and wants to perform a hypothesis test to determine whether the mean running time has changed as a result.

A)Lower-tailed
B)Upper-tailed
C)Two-sided

Question 5

An entomologist writes an article in a scientific journal which claims that fewer than 17% of male fireflies are unable to produce light due to a genetic mutation.

A) $H _ { 0 } : p < 0.17 , H _ { A } : p = 0.17$
B) $H _ { 0 } : p > 0.17 , H _ { A } : p = 0.17$
C) $H _ { 0 } : p = 0.17 , H _ { A } : p < 0.17$
D) $H _ { 0 } : p > 0.17 , H _ { A } : p < 0.17$
E) $H _ { 0 } : p = 0.17 , H _ { A } : p > 0.17$

Question 6

A manufacturer claims that the mean amount of juice in its 16 ounce bottles are 16.1 ounces.
A consumer advocacy group wants to perform a hypothesis test to determine whether the mean amount is actually less than this.

A)Lower-tailed
B)Two-sided
C)Upper-tailed

Question 7

A mayor is concerned about the percentage of city residents who express disapproval of his job performance.His political committee pays for a newspaper ad, hoping that it will keep the disapproval rate below 12%.They will use a follow-up poll to assess the ad's
Effectiveness.

A) $H _ { 0 } : p = 0.12 , H _ { A } : p > 0.12$
B) $H _ { 0 } : p > 0.12 , H _ { A } : p = 0.12$
C) $H _ { 0 } : p > 0.12 , H _ { A } : p < 0.12$
D) $H _ { 0 } : p = 0.12 , H _ { A } : p < 0.12$
E) $H _ { 0 } : p < 0.12 , H _ { A } : p = 0.12$

Question 8

A report on the U.S. economy indicates that $28 \%$ of Americans have experienced difficulty in making mortgage payments. A news organization randomly sampled 400 Americans from 10 cities named the "fastest dying cities in the U.S." (Forbes Magazine, August 2008) and found that 136 reported such difficulty. Does this indicate that the problem is more severe among these cities? The $P$ -value associated with the test statistic for testing this claim is $0.0029$ . At $\alpha = .05$ ,

A) We can conclude that the percentage of Americans in these cities experiencing difficulty making mortgage payments is equal to $28 \%$ .
B) We can conclude that the percentage of Americans in these cities experiencing difficulty making mortgage payments is not significantly different from $28 \%$ .
C) We can conclude that the percentage of Americans in these cities experiencing difficulty making mortgage payments is significantly lower than $28 \%$ .
D) We can conclude that the percentage of Americans in these cities experiencing difficulty making mortgage payments is significantly higher than $28 \%$ .
E) None of these

Question 9

Using the t-tables, software, or a calculator, estimate the critical value of t for the given Confidence interval and degrees of freedom: 98% confidence interval with df = 20

A)2.518
B)2.539
C)2.330
D)1.325
E)2.528

Question 10

Question 11

Question 12

The owner of a football team claims that the average attendance at games is over 74,900, and he is therefore justified in moving the team to a city with a larger stadium.An independent investigator will conduct a hypothesis test to determine whether his claim is accurate.

A)Lower-tailed
B)Upper-tailed
C)Two-sided

Question 13

A statistician consulting for a state department of transportation conducts a study to see if the proportion of drivers who are intoxicated has decreased since last year.
$H _ { 0 }$ : The proportion is the same as last year
$H _ { A } :$ The proportion is less than last year.
The P-value of a significance test is greater than the significance level.She can conclude:

A)the alternative hypothesis is true.
B)the null hypothesis is true.
C)there is not enough evidence to reject the null hypothesis.
D)the test was too powerful.

Question 14

Using the t-tables, software, or a calculator, estimate the critical value of t for the given confidence interval and degrees of freedom: 99% confidence interval with df = 24

A)2.492
B)2.797
C)2.807
D)2.779
E)1.711

Question 15

The manufacturer of a refrigerator system produces refrigerators that are supposed to maintain a true mean temperature, ?, of 48°F, ideal for certain beverages.The owner of a beverage company does not agree with the refrigerator manufacturer, and will conduct a hypothesis test to determine whether the true mean temperature differs from this value.

A)Two-sided
B)Upper-tailed
C)Lower-tailed

Question 16

Data in 1980 showed that about 40% of the adult population had never smoked cigarettes.In 2004, a national health survey interviewed a random sample of 2000 adults and found that 50% had never been smokers.Create a 95% confidence interval for the proportion of adults (in 2004) who had never been smokers.

A)Based on the data, we are 95% confident the proportion of adults in 2004 who had never smoked cigarettes is between 47.8% and 52.2%.
B)Based on the data, we are 95% confident the proportion of adults in 2004 who had never smoked cigarettes is between 37.4% and 52.2%.
C)Based on the data, we are 95% confident the proportion of adults in 2004 who had never smoked cigarettes is between 47.8% and 58.2%.
D)Based on the data, we are 95% confident the proportion of adults in 2004 who had never smoked cigarettes is between 40% and 60%.
E)Based on the data, we are 95% confident the proportion of adults in 2004 who had never smoked cigarettes is between 47.8% and 63.2%.

Question 17