Question

can I have solutions, please

1. A random sample of 144 observations has a mean of 20, a median of 21, and a mode of 22. The population standard deviation is known to equal 4.8. The 95.44% confidence interval for the population mean is

a. 15.2 to 24.8

b. 19.200 to 20.800

c. 19.216 to 20.784

d. 21.2 to 22.8

2. When the level of confidence decreases, the margin of error
   1. stays the same
   2. becomes smaller
   3. becomes larger
   4. becomes smaller or larger, depending on the sample size

3. A random sample of 64 students at a university showed an average age of 25 years and a sample standard deviation of 2 years. The 98% confidence interval for the true average age of all students in the university is a. 20.5 to 26.5

b. 24.4 to 25.6

c. 23.0 to 27.0

d. 20.0 to 30.0

4. A random sample of 49 statistics examinations was taken. The average score, in the sample, was 84 with a variance of 12.25. The 95% confidence interval for the average examination score of the population of the examinations is

a. 76.00 to 84.00

b. 77.40 to 86.60

c. 83.00 to 85.00

d. 68.00 to 100.00

5. The sample size needed to provide a margin of error of 2 or less with a .95 probability when the population standard deviation equals 11 is
   1. 10
   2. 11.
   3. 116
   4. 117

6. It is known that the population variance equals 484. With a 0.95 probability, the sample size that needs to be taken if the desired margin of error is 5 or less is
   1. 25
   2. 74
   3. 189
   4. 75

7. When constructing a confidence interval for the population mean and the standard deviation of the sample is used, the degrees of freedom for the t distribution equals
   1. n-1
   2. n
   3. 29
   4. 30

8. The following random sample from a population whose values were normally distributed was collected. 10     8          11           11

The 95% confidence interval for μ is a. 8.52 to 10.98

b. 7.75 to 12.25

c. 9.75 to 10.75

d. 8.00 to 10.00

9. The following random sample from a population whose values were normally distributed was collected. 10       12           18             16

The 80% confidence interval for μ is a. 12.054 to 15.946

b. 10.108 to 17.892

c. 10.321 to 17.679

d. 11.009 to 16.991

10. Which of the following best describes the form of the sampling distribution of the sample proportion?
    1. When standardized, it is exactly the standard normal distribution.
    2. When standardized, it is the t distribution.
    3. It is approximately normal as long as n ≥ 30.
    4. It is approximately normal as long as np ≥ 5 and n(1­p) ≥ 5.

Answer 1