A random sample of 13 items is drawn from a population whose standard deviation is unknown. The sample mean is x¯ = 950 and the sample standard deviation is s = 10. Use Appendix D to find the values of Student’s t. 1. Construct an interval estimate of mu with 99% confidence. (Round your answers to 3 decimal places.)
The 99% confidence interval is from to .
2. Construct an interval estimate of mu with 99% confidence, assuming that s = 20. (Round your answers to 3 decimal places.)
The 99% confidence interval is from to .
3. Construct an interval estimate of mu with 99% confidence, assuming that s = 40. (Round your answers to 3 decimal places.)
The 99% confidence interval is from to .

1. The 99% confidence interval is from 941.527 to 958.473

2. The 99% confidence interval is from 933.054 to 966.946

3. The 99% confidence interval is from 916.108 to 983.892

Step-by-step explanation:

The confidence interval is given by

Where is the sample mean and Margin of error is given by

Where n is the sample size,

s is the sample standard deviation,

is the t-score corresponding to some confidence level

The t-score corresponding to 99% confidence level is

Significance level = α = 1 - 0.99 = 0.01/2 = 0.005

Degree of freedom = n - 1 = 13 - 1 = 12

From the t-table at α = 0.005 and DoF = 12

t-score = 3.055

1. 99% Confidence Interval when s = 10

The margin of error is

So the required 99% confidence interval is

The 99% confidence interval is from 941.527 to 958.473

2. 99% Confidence Interval when s = 20

The margin of error is

So the required 99% confidence interval is

The 99% confidence interval is from 933.054 to 966.946

3. 99% Confidence Interval when s = 40

The margin of error is

So the required 99% confidence interval is

The 99% confidence interval is from 916.108 to 983.892

As the sample standard deviation increases, the range of confidence interval also increases.

step-by-step explanation:

always plug in x. in this case, x equals 4.

i'm going to first solve 4(2+3x)

1) 4(2+3(4)) use pemdas to solve.

i'm going to multiply whats in the parenthesis first, so 3 times 4=12.

2)4 (2+12) i'm then going to multiply 4 by both numbers in the parenthesis (because multiplying comes before adding)

4 times 2= 8.   4 times 12= 48

4) (8+48)= 56 (answer)

i'm then going to solve 8+12x and plug in 4 for x.

1) 8 +12(4)

multiplying comes before adding, so i'm gonna multiply 12 and 4.

12 times 4= 48.

2) 8+48=56

both equal the same!

b

step-by-step explanation: