Deck 10: Hypothesis Testing With Means and Proportions: The One-Sample Case

Question 1

What is the one-sample hypothesis test designed to do?

A) test whether the group represented by a sample differs from the population with respect to a given trait or characteristic
B) test whether an association in the population can be found if only one sample is taken from the population
C) test whether the initial sample taken from a population corresponds to a series of additional samples taken from the population
D) test whether the cells in a bivariate table are patterned differently from what random chance would suggest

Answer 1

test whether the group represented by a sample differs from the population with respect to a given trait or characteristic

Question 2

A null hypothesis of "no difference" is rejected at the 0.01 level. Which of the following is a valid conclusion?

A) that the null hypothesis is not true
B) that the odds are 1 to 1 that the correct decision has been made
C) that the odds are 10 to 1 that the correct decision has been made
D) that the odds are 100 to 1 that the correct decision has been made

Answer 2

that the odds are 100 to 1 that the correct decision has been made

Question 3

A veterinarian wants to know whether German Shepherd Dogs in Ontario are heavier or lighter than the average weight of that breed as documented in international records. Why will he probably use a one-sample hypothesis test?

A) Other types of hypothesis tests require a null hypothesis, but there cannot be one for this research scenario.
B) The scenario implies a one-tailed test, and only the one-sample hypothesis test allows this decision.
C) There is no population specified by this scenario, and one-sample hypothesis tests require only samples rather than populations.
D) It is more realistic for him to obtain a sample of Ontario German Shepherd Dogs than to obtain the population parameter.

Answer 3

It is more realistic for him to obtain a sample of Ontario German Shepherd Dogs than to obtain the population parameter.

Question 4

What does ì refer to in the null hypothesis for a one-sample test?

A) the probability of a Type I error
B) the mean of the population from which a sample is taken
C) the mean of a sample that is taken from a population
D) the mean of the difference between a sample score and the population's score

Question 5

A teacher wants to know if her students score better on a standardized test than the nationwide average. What would be an appropriate null hypothesis if she applied the one-sample test?

A) Students in her class do at least 1.5 times as well as the national average.
B) Students in her class do no better than the national average.
C) Students in her class fall short of the national average.
D) Students in her class do either better or worse than the national average.

Question 6

What does the research hypothesis (H₁) state in a one-sample hypothesis test?

A) The population does not have a certain characteristic.
B) The population is less than the sample value.
C) The sample is unlikely to be representative of the population.
D) The population value is unknown but likely to be large.

Question 7

What does the critical region represent in a one-sample hypothesis test?

A) the area under the curve that includes those values of a sample statistic that will lead to rejection of the null hypothesis
B) a confidence interval
C) a law that states that the shape of the sampling distribution is normal
D) the area under the curve that contains "non-rare" events

Question 8

If a Z (obtained) test statistic falls in the "critical region," what does this mean?

A) that it falls above the population mean (ì)
B) that it falls in an area of the sampling distribution near the mean of the sampling distribution
C) that it falls in an area of the sampling distribution that includes unlikely sample outcomes
D) that it falls in an area of the sampling distribution >Z = -1.96 and

Question 9

Which of the following may be concluded if the test statistic falls in the critical region in a one-sample test of significance?

A) that the research hypothesis is true
B) that the population distribution is normal
C) that the sample size was too small
D) that the null hypothesis can be rejected

Question 10

Suppose the test statistic obtained from a one-sample hypothesis test is 3.88, and the critical region begins at Z (critical) = ±1.96. Which of the following would be the correct conclusion?

A) fail to reject the null hypothesis
B) reject the null hypothesis
C) change the critical value to exceed the observed test statistic
D) redo the calculation because the observed test statistic is implausible

Question 11

Suppose that the test statistic from a one-sample hypothesis test does not fall in the critical region. Which of these statements would be a correct interpretation of this result?

A) The null hypothesis cannot be rejected.
B) The null hypothesis is false and the alternative hypothesis is true.
C) The null hypothesis is false and the alternative hypothesis is supported.
D) The alpha level should be changed.

Question 12

What is the Z (critical) value associated with a one-tailed test at alpha = 0.05?

A) 1.56
B) 1.65
C) 1.96
D) 2.56

Question 13

A researcher believes that the gender of fiction authors influences book sales online, but he is unwilling to say whether female writers have more new books sold or fewer new books sold relative to men. What would be the most appropriate type of research hypothesis in this case?

A) a one-tailed test
B) a skewness test
C) a symmetrical test
D) a two-tailed test

Question 14

What is the appropriate test of hypothesis for addressing the question of whether sex education classes and free clinics that offer counselling for teenagers reduce the number of pregnancies among teenagers?

A) a one-tailed test
B) a participant observation test
C) a two-tailed test
D) a cross-sectional test

Question 15

Under which of these circumstances can a one-tailed test of significance be used?

A) whenever the alpha level exceeds 0.10
B) whenever the researcher feels like it
C) whenever the researcher can predict a direction for the difference
D) whenever the null hypothesis is thought to be true

Question 16

What is a major difference between a one-tailed significance test and a two-tailed significance test?

A) For a given alpha level, Z (critical) is more extreme for the one-tailed test.
B) For a given alpha level, Z (critical) is less extreme for the one-tailed test.
C) The one-tailed test uses a test statistic, whereas the two-tailed test uses the critical region.
D) The two-tailed test uses a test statistic, whereas the one-tailed test uses the critical region.

Question 17

What happens if researchers specify a one-tailed hypothesis test, and the test statistic is large (e.g., Z = 3.5) but in the direction opposite of the alternative hypothesis?

A) The test is invalid.
B) The test should be conducted again, but at a different alpha level.
C) The null hypothesis cannot be rejected.
D) The null hypothesis is rejected in favour of the alternative hypothesis.

Question 18

When alpha is set at 0.05, which of these test scenarios will yield the largest absolute value for Z (critical)?

A) one-tailed test, upper tail
B) one-tailed test, lower tail
C) two-tailed test
D) The Z (critical) value will change only if alpha is changed.

Question 19

What is the alpha level at which a researcher would most likely reject the null hypothesis for a single-sample hypothesis test using the t sampling distribution?

A) 0.001
B) 0.01
C) 0.05
D) 0.10

Question 20

Suppose that we are conducting a one-tailed, single-sample, means significance test with alpha = 0.01 and with a sample of size n = 21. What would be the value for t (critical)?

A) 3.46
B) 2.85
C) 2.53
D) 1.72

Question 21

A researcher wants to conduct a single-sample hypothesis means test of significance, but ó is unknown. Assuming nothing is known about the population distribution, approximately how large must the sample be in order to justify using the t sampling distribution?

A) 25
B) 50
C) 100
D) 1000

Question 22

The value of t (obtained) is 1.78 for a two-tailed test with 60 degrees of freedom. What should be the conclusion of the test?

A) reject the null hypothesis
B) do not reject the null hypothesis
C) recalculate the test statistic with Z (observed)
D) A Type II error has been committed.

Question 23

What would be the appropriate sampling distribution for testing whether a sample of 450 Canadian households differs from the mean income of all Canadian households, where the population standard deviation is unknown?

A) t distribution
B) Z distribution
C) alpha distribution
D) null distribution

Question 24

Which of these t distributions will most resemble the Z distribution?

A) t distribution (df = 1.96)
B) t distribution (df = 25)
C) t distribution (df = 125)
D) All t distributions have an identical shape.

Question 25

We want to see whether a sample of engineering professionals (n = 330) differs in their licensing examination score from the population of engineers in a professional association. The population standard deviation is unknown. What would be the degrees of freedom for this test?

A) 1
B) 2
C) 329
D) 330

Question 26

Suppose a researcher wants to test whether a sample variable is different from the value in a population. The variable of interest is NOT interval-ratio. What should the researcher do?

A) conduct the single-sample hypothesis test for means
B) conduct the single-sample hypothesis test for proportions
C) calculate gamma
D) abandon any intention of hypothesis testing

Question 27

When might a researcher need to use proportions rather than means as the test statistic?

A) when the sample size is very large
B) when the sample size is very small
C) when the variable of interest is only interval-ratio in level of measurement
D) when the variable of interest is only nominal in level of measurement

Question 28

What would be the appropriate sampling distribution for testing whether a sample of 450 Canadian households differed in its average proportion of female members compared to the proportion of females in all Canadian households?

A) t distribution
B) alpha distribution
C) Z distribution
D) null distribution

Question 29

From a random sample size of 200 drawn from the suburbs of a large city, 120 respondents identify themselves as bilingual. For the whole metropolitan area, 75% of the residents classify themselves as bilingual. In this situation, what are the values for P_s and P_u respectively?

A) 0.60 and 0.50
B) 0.60 and 0.75
C) 120 and 0.75
D) 120 and 200

Question 30

From a random sample drawn from the suburbs of a large city, 60% of the respondents are bilingual. For the whole metropolitan area, 75% are bilingual. The difference between the sample and the population has been tested and the null hypothesis has been rejected. Which of the following may be concluded from these observations?

A) that the suburbs are significantly less likely to be bilingual
B) that the difference is not significant
C) that a one-tailed test has been used
D) that a Type I error has been committed

Question 31

The 95% confidence interval of a proportion ranges from 0.22 to 0.32. Our null hypothesis was that the sample proportion does not differ from the population proportion (P_u), which is 0.27. If our research hypothesis is two-tailed, what would we conclude about a sample proportion (P_s) equal to 0.33?

A) The research hypothesis should be rejected.
B) The null hypothesis should not be rejected.
C) The null hypothesis is likely true, but there is a 5% probability that it is actually false.
D) The null hypothesis should be rejected if alpha is set at 0.05.

Question 32

Suppose our null hypothesis is that a population mean is no different from 25. We calculate a 95% confidence interval, and the values range from 24 to 27. Which of the following should we conclude about the hypothesis test if we are using alpha = 0.05?

A) The null hypothesis should be rejected.
B) The null hypothesis should not be rejected.
C) The research hypothesis should be rejected.
D) It is impossible to evaluate a hypothesis with a confidence interval.

Question 33

Explain how confidence intervals can be used to convey the same information as a hypothesis test.

Question 34

A random sample of 123 students living in residence has been selected from the student body of a large university. The GPA for the student body as a whole is 2.59 and the mean for the sample is 2.47 with a standard deviation of 0.34. Is the difference statistically significant at the 0.05 level? Follow the five-step model and state all important decisions. Make sure that you interpret the results in terms of the original research question.

Question 35

A researcher selected a sample of 56 former co-op education students from a list of graduates of a university. She discovered that it had taken an average of 4.97 years for these graduates to finish their degrees (standard deviation = 1.23). The average for the entire student body is 4.56 years. Is the difference statistically significant at the 0.05 level? Follow the five-step model and state all important decisions. Make sure that you interpret the results in terms of the original research question.

Question 36

A researcher gathers a random sample of 300 kindergarten students from a local school district. A total of 86% of these students have their parents read them a book at home at least once per week. This is compared to a national estimate of 80%. Is the difference statistically significant at the level of alpha = 0.05? Follow the five-step model and state all important decisions. Make sure that you interpret the results in terms of the original research question.

Question 37

A researcher finds that 20% of adults drawn from a random sample in a neighbourhood (n = 326) have a university degree. She wants to know whether this neighbourhood is more educated than the overall city, where 16% of adults have a degree. Use 0.05 for alpha. Follow the five-step model and state all important decisions. Make sure that you interpret the results in terms of the original research question.