Z score for 97 confidence interval

1. (2 points) Two random samples are selected from two independent pop-

ulations. A summary of the samples sizes, sample means, and sample standard deviations is given below:

n1 = 37, x̄1 = 52.4, s1 = 5.8 n2 = 48, x̄2 = 75, s2 = 10

Find a 92.5% confidence interval for the difference µ1− µ2 of the means, assuming equal population variances.

Confidence Interval = Answer(s) submitted:

•

(incorrect)

2. (2 points) In order to compare the means of two popu- lations, independent random samples of 238 observations are selected from each population, with the following results:

Sample 1 Sample 2 x1 = 1 x2 = 3

s1 = 120 s2 = 200

(a) Use a 97 % confidence interval to estimate the difference between the population means (µ1−µ2).

≤ (µ1−µ2)≤ (b) Test the null hypothesis: H0 : (µ1− µ2) = 0 versus the al- ternative hypothesis: Ha : (µ1− µ2) 6= 0. Using α = 0.03, give the following:

(i) the test statistic z = (ii) the positive critical z score (iii) the negative critical z score The final conclustion is

• A. We can reject the null hypothesis that (µ1−µ2) = 0 and accept that (µ1−µ2) 6= 0. • B. There is not sufficient evidence to reject the null hy-

pothesis that (µ1−µ2) = 0.

(c) Test the null hypothesis: H0 : (µ1−µ2) = 26 versus the al- ternative hypothesis: Ha : (µ1−µ2) 6= 26. Using α = 0.03, give the following:

(i) the test statistic z = (ii) the positive critical z score (iii) the negative critical z score The final conclustion is

• A. We can reject the null hypothesis that (µ1−µ2) = 26 and accept that (µ1−µ2) 6= 26. • B. There is not sufficient evidence to reject the null hy-

pothesis that (µ1−µ2) = 26.

Answer(s) submitted:

• • • • • • • • • •

(incorrect)

3. (2 points) Two independent samples have been selected, 70 observations from population 1 and 83 observations from population 2. The sample means have been calculated to be x1 = 14.9 and x2 = 10.5. From previous experience with these populations, it is known that the variances are σ21 = 20 and σ22 = 21.

(a) Find σ(x1−x2). answer:

(b) Determine the rejection region for the test of H0 : (µ1−µ2) = 2.92 and Ha : (µ1−µ2)> 2.92 Use α = 0.05. z >

(c) Compute the test statistic. z =

The final conclustion is

• A. We can reject the null hypothesis that (µ1− µ2) = 2.92 and accept that (µ1−µ2)> 2.92. • B. There is not sufficient evidence to reject the null hy-

pothesis that (µ1−µ2) = 2.92. (d) Construct a 95 % confidence interval for (µ1−µ2).

≤ (µ1−µ2)≤ Answer(s) submitted:

• • • • • •

(incorrect)

4. (2 points) Randomly selected 100 student cars have ages with a mean of 7.2 years and a standard deviation of 3.4 years, while randomly selected 85 faculty cars have ages with a mean of 5.4 years and a standard deviation of 3.3 years.

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1. Use a 0.01 significance level to test the claim that student cars are older than faculty cars.

The test statistic is

The critical value is

Is there sufficient evidence to support the claim that student cars are older than faculty cars?

• A. Yes • B. No

2. Construct a 99% confidence interval estimate of the dif- ference µ1−µ2, where µ1 is the mean age of student cars and µ2 is the mean age of faculty cars.

< (µ1−µ2)< Answer(s) submitted: • • • • •

(incorrect)

5. (2 points) Randomly selected 15 student cars have ages with a mean of 7.9 years and a standard deviation of 3.4 years, while randomly selected 14 faculty cars have ages with a mean of 5.5 years and a standard deviation of 3.3 years.

1. Use a 0.05 significance level to test the claim that student cars are older than faculty cars.

(a) The test statistic is (b) The critical value is (c) Is there sufficient evidence to support the claim that stu-

dent cars are older than faculty cars?

• A. Yes • B. No

2. Construct a 95% confidence interval estimate of the dif- ference µs−µ f , where µs is the mean age of student cars and µ f is the mean age of faculty cars.

< (µs−µ f )< Answer(s) submitted: • • • • •

(incorrect)

7. (2 points) In which of the following scenarios will con- ducting a two-sample t-test for means be appropriate? CHECK ALL THAT APPLY.

• A. To test if the proportion of low-income families is higher than that of high-income families in British Columbia.

• B. To test if there is a difference between the mean an- nual income of husbands and that of wives in Canada.

• C. To test if the mean annual income of Ontarians is higher than that of British Columbians.

• D. To test if there is a difference between the propor- tion of low-income families in British Columbia and a known national proportion.

• E. To test if there is a difference between the mean annual income of male British Columbians and that of female British Columbians.

• F. To test if there is a difference between the mean annual income of British Columbians and a known na- tional mean.

• G. None of the above Answer(s) submitted: •

(incorrect)

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