Question

1. You have sampled 25 randomly selected students to find the mean test score. A 95% confidence interval for the mean came out to be between 85 and 92. Which of the following statements gives a valid interpretation of this interval?
1)If this procedure were to be repeated many times, 95% of the confidence intervals found would contain the true mean score.
2)If 100 samples were taken and a 95% confidence interval were found, 95 of them would be between 85 and 92
3)95% of the 25 students have a mean between 85 and 92

2. As standard deviation increases, samples size _____________ to achieve a specified level of confidence.
1) Increases 2)Decreases 3) No answer text provided.

3. In a manufacturing process a random sample of 9 bolts manufactured has a mean length of 3 inches with a standard deviation of 0.3. What is the 90% confidence interval for the true mean length of the bolt?
1) 2.8355 to 3.1645
2) 2.4420 to 3.5580
3) 2.814 to 3.1859

Answer 1

SOolution:

1) Answer = statement is

3)95% of the 25 students have a mean between 85 and 92

2. As standard deviation increases, samples size Increases to achieve a specified level of confidence.

3)

Point estimate = sample mean = =  

sample standard deviation = s = 0.3

sample size = n = 9

Degrees of freedom = df = n - 1 = 9-1 = 8

At 90% confidence level

= 1-0.90% =1-0.9 =0.10

/2 =0.10/ 2= 0.05

t/2,df = t0.05,8 = 1.86

t /2,df = 1.8595

Margin of error = E = t/2,df * (s /n)

= 1.8595 * (0.3 / 9)

Margin of error = E = 0.18595

The 90% confidence interval estimate of the population mean is,

- E < <  + E

3 -0.18595< < 3 + 0.18595

2.814 < < 3.1859

(2.814,3.1859)