Question

1. A researcher has gathered information from a survey of 25 randomly selected university campuses. From this data, it was reported that the average number of reported sexual assaults on these campuses in the last year was 12 with a standard deviation of 3. Calculate a 95% confidence interval to estimate the average number of sexual assaults on Canadian university campuses as a whole. Remember to report your confidence interval in a complete sentence and describe what it means. (15%)

2. A survey was conducted at Acadia on attitudes toward the campus alcohol policy against drinking games in residence with 262 randomly selected residence students. In response to the question, “Are you in favour of the drinking games policy?” 25% were in favour. What is the 99% confidence interval to estimate the percentage of all Acadia residence students regarding the drinking game policy? Remember to report your confidence interval in a complete sentence and describe what it means. (15%)

3. School boards in Nova Scotia, on average receive a budget of $623.00 per student from the provincial government. A random sample of 45 rural schools report that they received on average $605 per student with a standard deviation of $74. Is there a significant difference in the budgets between rural schools and the whole province? (20%)

This question is an example of statistical research using hypothesis testing. You will need to use the 5 step model of hypothesis testing to test for significance at a=.05.

• State assumptions

• State the null hypothesis and the alternative hypothesis
• State the appropriate hypothesis test for each question and determine your critical scores for testing significance at .05
• Calculate your test statistic making sure you show your formulas
• Interpret your results using complete sentences indicating is significance was determined

4. Nationally, the unemployment rate for teenage males is 18%. A random sample of 323 teenage males in your area reveals an unemployment rate of 21.7%. Are our local teens more likely to be unemployed?   (20%) This question is an example of statistical research using hypothesis testing. You will need to use the 5 step model of hypothesis testing to test for significance at a=.01.

• State assumptions

• State the null hypothesis and the alternative hypothesis
• State the appropriate hypothesis test for each question and determine your critical scores for testing significance at .01
• Calculate your test statistic making sure you show your formulas
• Interpret your results using complete sentences indicating is significance was determined

USING SPSS

5. What is the 99% confidence interval for the proportion of Canadians that have more than a high-school education? For this question you will need to use your data (your sample of Canadian) from the Canadian Community Health Survey. Use the variable (EDUDH04), create a new variable where 1=more than high school, and 0= every other VALID response. Calculate the statistics you need to construct your confidence internal, and then calculate the interval by hand by using the appropriate formula. (20%)

Copy and past a frequency table of your dummy variable (make sure your new variable is labelled) into your assignment. Copy and paste your statistics box. Write your answer in a complete sentence and describe what it means.

Answer 1

1)

Answer:

There is a 95% chance that the mean number of sexual assaults on Canadian university campuses lies in the interval (10.762,13.238).

Explanation:

The confidence interval for the mean is obtained using the formula,

Given:

Sample mean = 12

Sample Standard deviation = 3

The t critical value is obtained from t distribution table for significance level = 0.05 and degree of freedom = n -1 = 25 - 1 = 24.

2)

Answer:

There is a 99% chance that the proportion of Acadia residence students who favor the drinking games policy lies in the interval (0.181,0.319).

Explanation:

The confidence interval for the proportion is obtained using the formula,

Where,

3)

Assumptions:

The necessary assumptions to perform a hypothesis test is,

1) The data values should be continuous.

2) The samples should be randomly and independently selected

3) The population should be approximately normally distributed.

Hypothesis:

The Null and Alternative Hypotheses are,

This is a two-tailed test.

The significance level = 0.05

Hypothesis test and critical scores

Since we are comparing one sample mean with the population mean and the population standard deviation is unknown, the t-test for One Population Mean is used to test the hypothesis.

The critical value for the t statistic is obtained from the t critical value table for significance level = 0.05 and degree of freedom = n - 1 = 45 - 1 = 44

Test statistic

The t statistic is obtained using the formula,

Where,

Sample mean = 605

sample standard deviation = 74

Interpretation

Since the observed t statistic = -1.632 is less than the lower critical value = 2.015 at the 5% significance level, the null hypothesis is not rejected hence, it can be concluded that there is no difference in the budgets between rural schools and the whole province.

4)

Assumptions:

The necessary assumptions to perform a hypothesis test is,

1) The samples should be randomly and independently selected

2) The samples size should be less than 10% of the population (10% rule)

3) Normality assumption (such that )

Hypothesis:

The Null and Alternative Hypotheses are,

This is a right-tailed test.

The significance level = 0.01

Hypothesis test and critical scores

To test whether there is a significant difference in results from the survey, the z test for the one proportion is used.

The critical value for the z statistic is obtained from the standard normal distribution table for significance level = 0.01.

Test statistic

The z-statistic is obtained using the formula,

Where,

Hypothesized proportion = 0.18

Sample proportion = 0.217

Sample size = 323

Interpretation

Since the observed z statistic = 1.931 is less than the critical value = 2.33 at the 1% significance level, the null hypothesis is not rejected hence, hence there is no evidence to conclude that local teens more likely to be unemployed