Question

1.

Consider the folllowing data:

Description	Population 1	Population 2
Sample Mean	31.6	26.8
Population Variance	91.9	90.0
Sample Size	20	26

Construct a 99% confidence interval for the difference between population means.

(FORMATTING: Negative values should be indicated by a minus sign, no spaces! Round intermediate calculations to 6 decimal places and final answer to 2 decimal places).

a. Indicate the margin of error (6 decimal places):

b. Indicate the lower limit of the confidence interval (2 decimal places):

c. Indicate the upper limit of the confidence interval (2 decimal places):

d. Based on the confidence interval, can you conclude with 99% confidence that the population means are equal?

(Possible answers: "yes" or "no)

2.

Consider the folllowing competing hypotheses accompanying sample data drawn independently:

H_o: ?₁ - ?₂ ? 4

H₁: ?₁ - ?₂ < 4

Description	Population 1	Population 2
Sample Mean	242	269
Sample Standard Deviation	25	19
Sample Size	8	8

(FORMATTING: Negative values should be indicated by a minus sign, no spaces! Positive/Negative values should use the following format: "=-0.00". Round intermediate calculations to 6 decimal places and final answer to 2 decimal places).

a. Calculate the critical value using a 91% confidence level:

b. Calculate the value of the test statistic:

c. Calculate the p-value:

d. Do you have enough evidence to reject Ho at alpha level?

(only "yes" or "no").

3.

Consider the folllowing competing hypotheses accompanying sample data drawn independently:

H_o: ?₁ - ?₂ = 0

H₁: ?₁ - ?₂ ? 0

Description	Population 1	Population 2
Sample Mean	58	69
Population Standard Deviation	14.80	1.59
Sample Size	15	15

(FORMATTING: Negative values should be indicated by a minus sign, no spaces! Positive/Negative values should use the following format: "=-0.00". Round intermediate calculations to 6 decimal places and final answer to 2 decimal places).

a. Calculate the critical value using a 92% confidence level:

b. Calculate the value of the test statistic:

c. Calculate the p-value:

d. Do you have enough evidence to reject Ho at alpha level?

(only "yes" or "no").

Answer 1

Population 1:- Population 2:-

Sample Mean:-31.6 Sample Mean:-26.8

Pop Variance:-91.9 Pop Variance:-90.0

Sample size:-20 Sample Size:-26

Construct a 99% confidence interval for the difference between population means?

The point estimate for,

  

The standard error is,

  

The 99% confidence interval is,

Indicate the lower limit of the confidence interval (2 decimal places):   

Indicate the upper limit of the confidence interval (2 decimal places):

As this is a z-interval, we know that the correct value of z to use is 4.576. We interpret this interval that the difference between the two population means is 4.8 and we are 99% confident that the true mean lies between 17.91 and -8.191.

Based on the confidence interval, can you conclude with 99% confidence that the population means are equal?

Yes.

2)

Description	Population 1	Population 2
Sample Mean	242	269
Sample Standard Deviation	25	19
Sample Size	8	8

Calculate the value of the test statistic:

  

Calculate the critical value using a 91% confidence level:

Find Z_?/2 for 91% confidence.

91% written as a decimal is 0.91

1 - 0.91 = 0.09 = ? and ?/2 = 0.09/2 = 0.045

t- value is 2.10

With = .04 and df = 6, the critical value of t is 2.10. We reject H0 if t > 2.10

Here t < 2.10

We accept Ho

Do you have enough evidence to reject Ho at alpha level?

No