Statistical Inference Unit Test

In a hypothesis test, the alternative hypothesis is always a statement of equality. 

• True
• False

A Type I error is when: 

• We obtain the wrong test statistic
• We reject the null hypothesis when it is actually true
• We fail to reject the null hypothesis when it's actually false
• We reject the alternate hypothesis when it's actually true

A teacher in Math announced that the mean score of Grade 9 students in the first quarterly assessment in Mathematics was 89 and standard deviation was 6. One student, who believed that the mean score was less than this, randomly selected 30 students and computed the mean score. What kind of test of hypothesis can describe this?

• Left-tailed

• Two-tailed

• Right-tailed

• Multiple-tailed

Which of the following is the correct null and alternative hypotheses of the statement:

We want to test whether the general average of students in Math is different from 80%. .

• H₀: μ ≠ 80%, H_a: μ ≠ 80%

• H₀: μ = 80%, H_a: μ > 80%

• H₀: μ = 80%, H_a: μ ≠ 80%

• H₀: p = 80%, H_a: p ≠ 80%

Suppose the P-value for a hypothesis test is 0.0304. Using a = 0.05, what is the appropriate conclusion?

• a) Reject the null hypothesis

• b) Reject the alternative hypothesis

• c) Fail to reject the null hypothesis

• d) Fail to reject the alternative hypothesis

The average miles on a tank of gas for the Ford

Explorer is 300 miles with a standard deviation of 22

miles. A consumer group feels the average is actually

lower. They survey 40 vehicles and find the average

miles per tank is 290 miles. At α = 0.05, test the

consumer groups’ claim that the miles per tank is

actually lower than 300 miles.

• There is enough evidence to reject the claim

• There is not enough evidence to reject the claim

• There is enough evidence to support the claim

• There is not enough evidence to support the claim

A cereal company claims the mean sodium content in

one serving of its cereal is no more than 230 mg. You

work for a national health service and are asked to test

this claim. You find that a random sample of 52

servings has a mean sodium content of 232 mg and a

standard deviation of 10 mg. At α = 0.05, do you have

enough evidence to reject the company’s claim?

• Reject Ho

• Reject Ha

• Fail to reject Ho

• Fail to reject Ha

The Quick Stop claims that the Big Slurp will contain 48

ounces of drink. You decide to test this claim because

you feel the actual amount is lower. Over the next few

weeks, you buy 50 Big Slurps and find the average

amount of drink is 47 ounces with a standard deviation

of 2.75 ounces. At α = 0.05, can you reject the Quick

Stop’s claim?

• Reject Ho

• Reject Ha

• Fail to reject Ho

• Fail to reject Ha

A sample of 35 cans of Campbell’s Tomato Soup found

that the net weight of the cans was 298 grams with a

standard deviation of 24 grams. The production line

supervisor has been told that the net weight of all cans

is 308 grams. Is there enough evidence, at the 5% level,

to say that the weight of the cans is something other

than 308 grams?

• There is enough evidence to reject the claim

• There is not enough evidence to reject the claim

• There is enough evidence to support the claim

• There is not enough evidence to support the claim

The U.S. Department of Transportation reported that 77% of all fatally injured automobile drivers were intoxicated. A random sample of 27 records of automobile driver fatalities in Kit Carson County, Colorado, showed that 15 involved an intoxicated driver. Carson County believes their proportion is lower than the national average. Which p-value for this test?(use 5:1 prop Z test)

• p = 0.996

• p = 0.004

• p = 0.008

• p = -2.64