Question

1. For a Normal distribution N (μ, σ), if we know the population standard deviation then we can make an inference about:

1. Mode

2. Range

3. Mean

4. Median

2. The Normal Distribution curve of heights of a large population of people indicates that the mean height (μ) of the population is 5 feet 6 inches. The 1 standard deviation (σ) in height variation is 2 inches. The people who have the heights between 5 feet 2 inches and 5 feet 10 inches represent:

   1. the range of +1σ to -1 σ

   2. the range of +2σ to -2 σ

   3. the range of +3σ to -3 σ

3. The Normal Distribution curve of heights of a large population of people indicates that the mean height (μ) of the population is 5 feet 3 inches. The 1 standard deviation (σ) in height variation is 2 inches. The people who have the heights between 4 feet 11 inches and 5 feet 7 inches represent:

   1. the range of +2σ to -2 σ

   2. the range of +σ to -σ

   3. the range of +3σ to -3 σ

20. The Normal Distribution curve of heights of a large population of people indicates that the mean height (μ) of the population is 5 feet 5 inches. The 1 standard deviation (σ) in height variation is 2 inches. The people who have the heights between 5 feet 3 inches and 5 feet 7 inches represent:

    1. the range of +2σ to -2 σ

    2. the range of +σ to -σ

    3. the range of +3σ to -3 σ

CENTRAL LIMIT THEOREM (Sampling Distribution)

28. According to the Central Limit Theorem , as the SRS increases, that is as n INCREASES, the sample mean is

1. Closer to the population mean µ

2. Away from the population mean µ

29. According to the Central Limit Theorem, as the SRS increases, that is as n INCREASES, the sample distribution becomes

1. Left-skewed distribution

2. Right-skewed distribution

3. Normal Distribution

A random survey test was given to 100 students. The average score (mean) x was 75. The standard deviation, σ, was 20. Answer the following questions based on this information. Note: n = 100 and look at PPT on Confidence Interval posted on BB.

30. The ‘Law of Large Numbers’ states that as no. of observations drawn INCREASES, the observed mean gets closer to the

1. Standard deviation of the population

2. Probability of the population

3. Mean of the population

31. The standard deviation of a Normal Distribution of IQ of a population of adults is 15. For a simple random size (SRS) of 9 from this population, the standard deviation for the sampling distribution will be:

1. 15

2. 15/9

3. 9

4. 5

32. The 95%-confidence interval means that we got these numbers using a method that gives CORRECT results …… of the times.

1. 68%

2. 100%

3. 99.7%

4. 95%

33. The 95%-confidence interval means that the MARGIN OF ERROR is only:

1. 95%

2. 5%

3. 68%

4. 99.7%

34. The margin of error for a sample of n =1000 will be ……. for a sample of n =50.

1. Less than

2. Greater than

3. Equal to

35. For a sample size of ‘N’ the degrees of freedom for some statistical tests can be computed from the formula:

1. N-5

2. N-2

3. N-3

4. N-4

HYPOTHESIS TESTING (Read the chapter and you will find the answers)

36. A Hypothesis always refers to a …….of population.

1. Mean

2. Standard deviation

37. The hypothesis that “The more beer you drink…the higher your blood alcohol level will be” an example of:

    1. Null Hypothesis

    2. Alternative Hypothesis

38. The value of α = 0.05 means that we are requiring that data give evidence AGAINST the Null Hypothesis so strong that it would happen ……… of the time.

1. No more than 95%

2. No less than 95%

3. No more than 5%

4. No less than 50%

Answer 1

• For normal distribution if we know the population standard deviation then we can draw inference about mean.

• Mean height = 5 ft 6 inches = 66 inches.

standard deviation = 2 inches.

The people who have the heights between 5 feet 2 inches and 5 feet 10 inches represent:

the range of +2σ to -2 σ

Reason : mean height - 2*standard deviation = 66-2*2 = 62 = 5 ft 2 inches.

mean height + 2*standard deviation = 66+2*2 = 70 = 5 ft 10 inches.

• Mean height = 5 ft 3 inches = 63 inches.

standard deviation = 2 inches.

The people who have the heights between 4 feet 11 inches and 5 feet 7 inches represent:

the range of +2σ to -2 σ

Reason : mean height - 2*standard deviation = 63-2*2 = 59 = 4 ft 11 inches.

mean height + 2*standard deviation = 63+2*2 = 67 = 5 ft 7 inches.

• Mean height = 5 ft 5 inches = 65 inches.

standard deviation = 1 inches.

The people who have the heights between 5 feet 3 inches and 5 feet 7 inches represent:

the range of +σ to - σ

Reason : mean height - 2*standard deviation = 65-1*2 = 63 = 5 ft 3 inches.

mean height + 2*standard deviation = 65+1*2 = 67 = 5 ft 7 inches.

According to the Central Limit Theorem , as the SRS increases, that is as n INCREASES, the sample mean is

Closer to the population mean µ.

Since if we increase the sample size then we are approaching the population and hence we are closer to the population mean.

According to the Central Limit Theorem, as the SRS increases, that is as n INCREASES, the sample distribution becomes

Normal Distribution