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Stats Final Exam 3rd Qtr 2025

Total questions: 42

Worksheet time: 4hrs 30mins

Name
Class
Date
1.

What kind of hypothesis test would you use?

  1. A random sample of 49 medical doctors in LA showed that they worked an average of 53.1 hours/week with a standard deviation of 7.2 hours/week. If the California average is 60 hours/week, does this give evidence that the LA doctors work  significantly less than the rest of California?

a)

1 Proportion z test

b)

1 sample t test

c)

1 sample z test

d)

None of these

2.

Select the correct null and alternate hypothesis

  1. A random sample of 49 medical doctors in LA showed that they worked an average of 53.1 hours/week with a standard deviation of 7.2 hours/week. If the California average is 60 hours/week, does this give evidence that the LA doctors work  significantly less than the rest of California?

a)

Ho: p = 60

Ha: p < 60

b)

Ho: μ\mu = 60

Ha: μ\mu < 60

c)

Ho: μ = 53.1

Ha : μ < 53.1

d)

None of these

3.

USA Today reported that in 1992, 39% of all elementary school children claimed that when they grow up they want to  do something to help other people. However, in 1995, 128 of a random sample of 317 of these same children claimed  that when they grow up they want to do something to help other people. Does this information indicate that the  proportion has increased? Suppose α = 0.05.

a)

1 Proportion z test

b)

1 sample t test

c)

1 sample z test

d)

1 Proportion z interval

4.

Choose the correct set of hypothesis

USA Today reported that in 1992, 39% of all elementary school children claimed that when they grow up they want to  do something to help other people. However, in 1995, 128 of a random sample of 317 of these same children claimed  that when they grow up they want to do something to help other people. Does this information indicate that the  proportion has increased? Suppose α = 0.05.

a)

Ho: p = .39

Ha : p > .39

b)

Ho: p = .40

Ha : p > .40

c)

Ho: μ = .39

Ha : μ > .39

d)

Ho: μ = .40

Ha : μ > .40

5.

What kind of hypothesis test would you use?

A psychologist claims that the mean age at which children start walking is 12.5 months. The following data give the age  at which 18 randomly selected children started walking.  

15 11 13 14 15 12 15 10 16 17 14 16 13 15 15 14 11 13 

Test at the 1% level of significance if the mean age at which children start walking is different from 12.5.

a)

1 Proportion z test

b)

1 sample t test

c)

1 sample z test

d)

1 sample t interval

6.

Which would be equivalent to the hypothesis test in the previous question?

A psychologist claims that the mean age at which children start walking is 12.5 months. The following data give the age  at which 18 randomly selected children started walking.  

15 11 13 14 15 12 15 10 16 17 14 16 13 15 15 14 11 13 

Test at the 1% level of significance if the mean age at which children start walking is different from 12.5.

a)

A 90% confidence interval with 𝛂=.10

b)

A 99.5% confidence interval with 𝛂=0.005

c)

A 99% confidence interval with 𝛂=.01

d)

No confidence interval would be appropriate here.

7.

What kind of hypothesis test would you use?

The population standard deviation for waiting times to be seated at a restaurant is known to be 10 minutes. An  expensive restaurant claims that the average waiting time for dinner is approximately 1 hour, but we suspect that this  claim is inflated to make the restaurant appear more exclusive and successful. A random sample of 30 customers yielded  a sample average waiting time of 50 minutes. Is there evidence to say that the restaurant’s claim is too high? 

a)

1 Proportion z test

b)

1 sample t test

c)

1 sample z test

d)

1 sample z interval

8.

What kind of hypothesis test would you use?

  1. In a survey of 1273 adults, 52% said it is not morally wrong to change the genetic makeup of human cells. What test would be indicated to address the following statement: “The majority of adults do not think it is morally wrong to  change the genetic makeup of human cells”

a)

1 Proportion z test

b)

1 sample t test

c)

1 sample z test

d)

1 sample z interval

9.

Choose the correct set of hypothesis for this question

  1. In a survey of 1273 adults, 52% said it is not morally wrong to change the genetic makeup of human cells. What test would be indicated to address the following statement: “The majority of adults do not think it is morally wrong to  change the genetic makeup of human cells”

a)

Ho: μ = .50

Ha: μ > .50

b)

Ho: pp =.50

Ha: p>.50p>.50

c)

Ho: phat = .52

Ha: phat > .52

d)

Ho: p = .52

Ha: p > .52

10.

Which is not a condition for the previous test?

  1. In a survey of 1273 adults, 52% said it is not morally wrong to change the genetic makeup of human cells. What test would be indicated to address the following statement: “The majority of adults do not think it is morally wrong to  change the genetic makeup of human cells”

a)

np≥10

b)

SRS

c)

n≥30

d)

at least 12,730 adults in the population

11.

What kind of hypothesis test would you use?

Your company sells exercise clothing and equipment on the Internet. To design the clothing, you collect data on the  physical characteristics of your different types of customers. We take a sample of 24 male runners and find their mean  weight to be 61.79 kilograms. Assume that the population standard deviation is σ = 4.5.

a)

1 Proportion z test

b)

1 sample t test

c)

1 sample z test

d)

None of these

12.

Which is NOT a condition for the test in the previous question?

Your company sells exercise clothing and equipment on the Internet. To design the clothing, you collect data on the  physical characteristics of your different types of customers. We take a sample of 24 male runners and find their mean  weight to be 61.79 kilograms. Assume that the population standard deviation is σ = 4.5.

a)

SRS

b)

Sample size should be greater than or equal to 30, or come from a known normal distribution, or have know outliers or skewness in the data

c)

We need to know σ

d)

np≥10, n(1-p)≥10

13.

A teacher is interested in performing a hypothesis test to compare the mean math score of the girls and the mean math score of the boys. She randomly selects 10 girls from the class and then randomly selects 10 boys. She arranges the girls' names alphabetically and uses this list to assign each girl a number between 1 and 10. She does the same thing for the boys.

a)

1-sample t-test. The teacher should compare the sample mean for the girls against the population mean for the boys.

b)

Paired t-test. Since the boys and girls are in the same class, and are hence dependent samples, they can be linked.

c)

Either two-sample or paired t-test will work.

d)

Two-sample t-test. There is no natural pairing between the two populations.

e)

Paired t-test. Since there are 10 boys and 10 girls, we can link the two samples.

14.

A researcher is interested in investigating whether people perform better at dexterity tests while listening to classical music or to no music. He designs a dexterity test, and first gives it to his participants while classical music is playing, and then while no music is playing.

a)

z-test, since the researcher can find the standard deviation of his population.

b)

Not enough information is given to determine the best type of test.

c)

Paired t-test, since there are two sets of measurements on the same subjects, providing a natural linking.

d)

Two-sample t-test, since how a subject performs with music should have no influence on how he performs without music, creating two independent samples.

e)

1-sample t-test, since there is only one sample of subjects taking the dexterity tests.

15.

An agricultural company wanted to know if a new insecticide would increase corn yields. Eight test plots showed an average increase of 3.125 bushels per acre. The standard deviation of the increases was 2.911 bushels per acre. Determine a 99% confidence interval for the mean increase in yield.

a)

(-0.476, 6.726)

b)

(-6.726, -4.399)

c)

(-0.476, 4.399)

d)

(1.851, 6.726)

e)

(1.851, 4.399)

16.

A coach uses a new technique in training middle distance runners. The times for 9 different athletes to run 800 meters before and after this training are shown. Construct a 99% confidence interval for the mean difference

a)

(-6.42, 8.87)

b)

(-0.76, 3.20)

c)

(-0.85, 3.29))

d)

(-0.54, 2.98)

e)

(-0.82, 3.27)

17.

A high school coach uses a new technique in training middle distance runners. He records the times for 4 different athletes to run 800 meters before and after this training. A 90% confidence interval for the difference of the means before and after the training, μB - μA, was determined to be (2.6, 4.8).

a)

We know that 90% of all random samples done on runners at this high school will show that the mean time difference before and after the training is between 2.6 and 4.8 seconds.

b)

There is a 90% probability that a randomly selected middle distance runner at this high school will have a time for the 800-meter run that is between 2.6 and 4.8 seconds shorter after the training than before the training.

c)

Based on this sample, with 90% confidence, the average time for the 800-meter run for middle distance runners at this high school is between 2.6 and 4.8 seconds shorter after the new training.

d)

We know that 90% of the middle distance runners shortened their times between 2.6 and 4.8 seconds after the training.

e)

Based on this sample, with 90% confidence, the average time for the 800-meter run for middle distance runners at this high school is between 2.6 and 4.8 seconds longer after the new training.

18.

Five students took a math test before and after tutoring. Their scores were as follows. Do the data suggest that there is a difference in the math scores? Perform a paired t-test at the 5% significance level.

a)

No, the data do not provide sufficient evidence to conclude that the tutoring has an effect on the math scores.

b)

Yes, the data do provide sufficient evidence to conclude that the tutoring has an effect on the math scores.

19.

Which of the following represents the appropriate null & alternative hypotheses?

The mean height of women is greater than 64"

a)

H₀: μ > 64"

Hₐ: μ ≠ 64"

b)

H₀: μ < 64"

Hₐ: μ > 64"

c)

H₀: p > 64"

Hₐ: p ≠ 64"

d)

H₀: p = 64"

Hₐ: p > 64"

20.

Identify the correct null hypothesis:


Is the proportion of babies born male different from 50%? In a sample of 200 babies, 96 were male. Test the claim using a level of significance of 1%.

a)

H0: p = 0.50

b)

H0: µ = 100

c)

H0: p = 0.48

d)

H0: µ = 96

21.
When performing a test about the population proportion, what distribution would you need to use? 
a)
z
b)
t
c)
chi-square
22.
Which of the following shows a right-tailed test?
a)
Ha: µ < 15
b)
H0: µ < 15
c)
Ha: µ > 15
d)
H0: µ > 15
23.
In testing hypotheses, which of the following would be strong evidence against the null hypothesis?
a)
using a small level of significance
b)
using a large level of significance
c)
obtaining data with a small p-value
d)
obtaining data with a low test statistic
24.
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 obtaining the results (or one more extreme) if the null hypothesis is true
d)
probability of a Type I error
25.

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

a)

a) Reject the null hypothesis

b)

b) Reject the alternative hypothesis

c)

c) Fail to reject the null hypothesis

d)

d) Fail to reject the alternative hypothesis

26.

When p-value is greater than alpha we:

a)

Reject Ho

b)

Fail to reject Ha

c)

Fail to reject Ho

d)

Reject Ha

27.

What is the FORMULA for the ONE SAMPLE zz  -TEST?

a)

z=x‾−μσnz=\frac{\overline{x}-\mu}{\frac{\sigma}{\sqrt[]{n}}}  

b)

t=x‾−μsnt=\frac{\overline{x}-\mu}{\frac{s}{\sqrt[]{n}}}  

c)

z=x‾1−x‾2σ12n1+σ22n2z=\frac{\overline{x}_1-\overline{x}_2}{\sqrt[]{\frac{\sigma_1^2}{n_1}+\frac{\sigma_2^2}{n_2}}}  

d)

None of these

28.

What is the FORMULA for the ONE SAMPLE tt  -TEST?

a)

z=x‾−μσnz=\frac{\overline{x}-\mu}{\frac{\sigma}{\sqrt[]{n}}}  

b)

t=x‾−μsnt=\frac{\overline{x}-\mu}{\frac{s}{\sqrt[]{n}}}  

c)

z=x‾1−x‾2σ12n1+σ22n2z=\frac{\overline{x}_1-\overline{x}_2}{\sqrt[]{\frac{\sigma_1^2}{n_1}+\frac{\sigma_2^2}{n_2}}}  

d)

None of these

29.

What is the FORMULA for the DIFFERENCE OF MEANS: LARGE INDEPENDENT SAMPLES?

a)

z=x‾−μσnz=\frac{\overline{x}-\mu}{\frac{\sigma}{\sqrt[]{n}}}  

b)

t=x‾−μsnt=\frac{\overline{x}-\mu}{\frac{s}{\sqrt[]{n}}}  

c)

z=x‾1−x‾2σ12n1+σ22n2z=\frac{\overline{x}_1-\overline{x}_2}{\sqrt[]{\frac{\sigma_1^2}{n_1}+\frac{\sigma_2^2}{n_2}}}  

d)

None of these

30.
Which test would you use to see if the distribution of music that Californians listen to is the same as that of Nevadans?  900 Californians and 600 Nevadans were surveyed.
a)
Chi-square Goodness of Fit Test
b)
Chi-Square Test for Homogeneity
c)
Chi-Square Test for Independence/Association
d)
Not a Chi-square test
31.
Which test would you use .... In 1974, each acre of the Tahoe basin was assessed to see what condition the soil was in.  23% of acres were of type I, 32% were of type II, 41% were of type III, and 16% were of type IV.  This year the region was assessed again and the number of each type were again determined.
a)
Chi-square Goodness of Fit Test
b)
Chi-Square Test for Homogeneity
c)
Chi-Square Test for Independence/Association
d)
Not a Chi-square test
32.
Which test would you use to see if gender is a factor choosing a person’s favorite fruit?  900 college students were surveyed and their favorite fruit recorded.
a)
Chi-square Goodness of Fit Test
b)
Chi-Square Test for Homogeneity
c)
Chi-Square Test for Independence/Association
d)
Not a Chi-square test
33.
Which test would you use to see whether the fans that buy tickets are demographically the same as the general population of the city.  Currently 42% are Caucasian, 35% are Hispanic, 12% are African American, 8% are Asian, and the rest are defined as other.
a)
Chi-square Goodness of Fit Test
b)
Chi-Square Test for Homogeneity
c)
Chi-Square Test for Independence/Association
d)
Not a Chi-square test
34.
Which test would you use to see if shoe brand preferences changed between last year and this year?  1000 people were observed this year and last year to see what brand of shoe they were wearing.
a)
Chi-square Goodness of Fit Test
b)
Chi-Square Test for Homogeneity
c)
Chi-Square Test for Independence/Association
d)
Not a Chi-square test
35.

What is the expected value of a female who likes Pepsi?

a)

10.5

b)

11

c)

14.5

d)

6.3

36.

What is the

χ2 calculated value for the following situation.

a)

6.65

b)

6.66

c)

0.00991

d)

1

37.

What are the degrees of freedom for the following χ² test?

a)

6

b)

2

c)

5

d)

12

38.
The bigger the chi square statistic, the ________ the p value.
a)
bigger
b)
smaller
39.

Is the type of television show that a person chooses to watch related to the brand of deodorant that a person uses? 1500 people were surveyed.

a)

Chi-square Goodness of Fit Test

b)

Chi-Square Test for Independence

c)

Chi-squared test for correlation

d)

Not a Chi-square test

40.

What must be true about the expected values in a chi square test?

a)

greater than or equal to 2

b)

greater than or equal to 5

c)

greater than or equal to 10

d)

greater than or equal to 30

41.

Using a Graphing Calculator, the chi-square test statistic for commuter data is χ² = 5.37 with P-value < 0.01. If we use α=0.05\alpha=0.05  , what conclusion is appropriate?

a)

Do NOT reject H0; the results are significantly different.

b)

Do NOT reject H0; the results are not significantly different.

c)

Reject H0; the results are significantly different

d)

Reject H0; the results are not significant different.

42.
The table shows the number or babies born on each day of the week.  Is there evidence that births are more likely on specific days of the week?
a)
yes, the p value is greater than .05
b)
no, the p value is less than .05
c)
yes, the p value is less than .05
d)
no, the p value is greater than .05

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