Download Worksheet on Using Critical Values

Critical Values
Name______________________
Directions: Write the hypotheses & formula. Find the critical value and test statistic. Tell R or F.
1.
The CEO of the company claims that the mean work day of the company’s mechanical engineers is less than 8.5
hours. A random sample of 35 of the company’s mechanical engineers has a mean work day of 8.2 hours. The
standard deviation is known to be 0.5 hours. Test the CEO’s claim using a 1% significance level.
2.
An organization believes that the number of prospective home buyers who want their next house to be larger,
smaller, or the same size as their current house is uniformly distributed. Test using a 5% level of significance.
Response
Larger
Same size
Smaller
Freq
285
224
291
3.
A repair shop believes that people travel more than 3500 miles between oil changes. A random sample of 8 cars
getting an oil change has a mean distance of 3375 miles since having an oil change with a standard deviation of 225
miles. At = 0.05, do you have enough evidence to support the shop’s claim?
4.
A nutritionist claims that a particular exercise program will help participants lose weight after one month. At  =
0.10, can you conclude that the exercise program helps participants lose weight?
Participant
Before
After
5.
1
157
150
2
185
181
3
120
121
4
212
206
5
230
215
6
165
169
7
207
210
8
251
232
9
196
188
10
140
138
The scoring averages (in points per game) of 8 professional basketball players for their rookie and sophomore
seasons are shown below. At  = 0.05, is there enough evidence to conclude that the scoring averages have change?
Participant
Rookie
Sophomore
1
18.5
17.5
2
13.9
14.7
3
16.1
16.9
4
15.3
16.3
5
16.8
20.4
6
13
18.9
7
11.9
14.6
8
11.8
6.3
6.
A medical researcher says that less than 25% of U.S. adults are smokers. In a random sample of 200 U. S. adults,
18.5% say that they are smokers. At  = 0.05, is there enough evidence to reject the researcher’s.
7.
A county is considering raising the speed limit on a road because they claim that the mean speed of vehicles is
greater than 45 miles per hour. A random sample of 25 vehicles has a mean speed of 48 miles per hour and a
standard deviation of 5.4 miles per hour. At  = 0.10, do you have enough evidence to support the county’s claim?
8.
To compare the braking distances for two types of tires, a safety engineer conducts 50 braking tests for each type.
Type A had a mean braking distance of 55 ft with a standard deviation of 5.3 ft. Type B had a mean braking
distance of 51 ft with a standard deviation of 4.9 ft. At  = 0.10, can the engineer support the claim that the mean
breaking distance for Type A is greater than the mean braking distance for Type B.
9.
A medical research team conducted a study to test the effect of a migraine drug. Of the 400 subjects who took
the drug, 65% were free of nausea after two hours. Of the 407 subjects who took a placebo, 53% were free of
nausea after two hours. At  = 0.10, can you support the claim that the proportion of subjects who are fee of
nausea is greater for subjects who took the drug than for subjects who took a placebo?
10. The following shows how a random sample of adults rated a newly released movie and gender. Can you conclude that
the adults’ ratings are related to gender?
Male
Female
Excellent
97
101
Good
42
33
Fair
26
25
Poor
5
11