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

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?

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

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 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.

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?

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

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?

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

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?

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?

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?

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

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

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?

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

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 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.