# Hypothesis Testing Using Independent Samples and T Distribution

As a counsellor in the field of addiction, you are interested in researching if online gambling is becoming more prevalent. You decide to conduct research to compare online gambling to gambling in public places such as casinos. You hypothesize that online gambling is more prevalent among those who are under the age 30, leading to more online gambling addictions in those individuals who are under 30. To test your hypothesis, you use a random sample of 40 individuals who report attending counselling because of a gambling addiction. The ages of the individuals and initial mode of gambling was recorded. The ages for those who gamble online and in public are shown in the table. On the basis of the data provided, can you conclude that online gambling is more prevalent among individuals who are under the age of 30 at a level of significance of 0.05? Why or why not? (Show all seven steps of the appropriate hypothesis test.) Refer to the chart in the attached document.

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#### Solution Preview

We need to perform a hypothesis testing to test if online gambling is more prevalent among individuals who are under the age of 30 at a level of significance of 0.05.

The null hypothesis: online gambling is not more prevalent among individuals who are under the age of ...

#### Solution Summary

The solution gives detailed steps on conducting hypothesis testing for two independent samples using t distribution from a real example on gambling.

10 Multiple choice questions on Hypothesis testing, distributions.

Please see the attached file for full problem description.

1. If standard deviation (sigma) is unknown when completing a hypothesis test about the population mean, then the best estimate for the unknown standard deviation is s. _____ T/F

2. The chi-square distribution is used for inferences about the population mean (mu) when the standard deviation (sigma) is unknown. ____ T/F

3. The t-distribution is used for all inferences about a population's variance. ___ T/F

4. When the means of two unrelated samples are used to compare two populations, we are dealing with two dependent means ___ T/F

5. Pretest versus post-test (before versus after) studies are usually independent samples. ____ T/F

6. The number of degrees of freedom for the critical value of t is equal to the smaller of n1 -1 or n2 -1 when making inferences about the difference between two independent means for the case when the degrees of freedom are estimated. ___ T/F

7. The F distribution is a symmetric distribution. ____ T/F

8. Which of the following would be the correct null hypotheses for testing the claim that the proportion of make students (M) who smoke at a particular college is greater than the proportion of female students (F) who smoke?

A. H0: pM (greater than or equal to) pF

B. H0: pM (less than or equal to) pF

C. H0: pM > pF

D. H0: pM < pF

9. Which of the following would be the correct hypotheses for testing the claim that the mean waiting time to be served at a large post office is at least 6.5 minutes?

A. H0: (mu) (greater than or equal to) 6.5 and Ha: (mu) < 6.5

B. H0: (mu) = 6.5 and Ha: (mu) (not equal to) 6.5

C. H0: (mu) (less than or equal to) 6.5 vs. Ha: (mu) > 6.5

D. H0: (mu) > 6.5 vs. Ha: (mu) (greater than or equal to) 6.5

10. The mean age of 25 randomly selected college seniors was found to be 23.5 years, and the standard deviation of all college seniors was 1.3 years. Which of the following is the correct symbol for 1.3 years?

A. (mu) B. s C. (sigma) D. X bar