Statistics and Probability Answers

Of two similar groups of patients, A and B, consisting of 50 and 100 individuals, respectively, the first was

given a new type of sleeping pill and the second was given a conventional type. For patients in group A the

mean number of hours of sleep was 7.82 with a standard deviation of 0.24 hour. For patients in group B the

mean number of hours of sleep was 6.75 with a standard deviation of 0.30 hour. Find (a) 95% and (b) 99%

confidence limits for the difference in the mean number of hours of sleep induced by the two types of

sleeping pills.

Consider all samples of size 5 from this population. 

2,5,6,8,10,12,13

1. Compute the mean and the standard deviation of the population. 

2. List all samples of size 5 and compute the mean for each sample. 

3. Construct the sampling distribution of the sample means.

4. Calculate the mean of the sampling distribution of the sample means. 

Compare this to mean of the population. 

5. Calculate the standard deviation of the sampling distribution of the 

sample means . Compare this to the standard deviation of the 

population. 

Question 1

Using practical examples from the field of statistics, determine the following variables you expect to have a normal or nearly normal distribution. Illustrate by discussing and explaining possible reasons for your answer.

a. Scores on a very easy test

b. Shoe sizes of a random sample of adult women

c. The number of apples in each of 100 full bushel baskets

find the point estimate of the population parameter μ, and the standard deviation for each of the following sets of data. show your computations.

weights (in grams) of packed ground coffee:

350 346 350 346 350 348 351 351

340 347 344 340 340 340 345 347

355 348 351 355 347 352 356 352

347 348 347 347 347 347 346 347

348 351 347 348 348 348 348 349

348 349 348 348 349 348 347 349

349 349 349 349 349 348 346 349

time (in seconds) it took Lydia to finish a 100m practice race:

15 12 16 12 15 15 15 16

14 13 14 14 16 14 14 16

12 12 12 13 12 15 12 13

12 15 15 13 12 12 12 12

15 11 15 15 15 15 15 15

18 16 17 16 15 16 16 18

18 17 18 16 15 14 18 16

Percentage of children who watch tv before bedtime:

70 67 58 60 69 69 70 62

69 59 77 59 52 79 59 59

80 42 60 59 68 40 68 68

56 66 60 40 57 57 70 71

72 54 52 67 62 59 71 72

81 49 45 78 78 69 68 69

Percentage of parents in favor of including cultural values in the mathematics curriculum:

90 70 80 76 81 82 76 84

89 59 76 78 75 89 79 89

92 42 58 84 75 90 80 78

82 68 82 82 68 78 79 80

72 54 83 80 78 79 80 84

81 69 78 78 80 82 81 90

Question 1) In each of the following situations, identify the population and the sample

(i). There are 50 books in statistics in our library which contains a collection of 5,000 books.

(ii). About 20% of the stones heaped on the building site are round in shape.

(iii). The dream that there will be more female than male politicians in Ghana will never be realized

(iv) About 10% of pregnant mothers reporting to hospitals are infected with HIV virus.

(v) Since the last major earthquake in 1939, there have been 60 earth tremors in Ghana, with 20 these occurring over the past 5 years.

find the point estimate of the population parameter μ, and the standard deviation for each of the following sets of data. show your computations.

1. scores in a long test in science:

78 75 86 82 70 85 83 86

80 92 82 85 80 80 84 86

90 88 90 78 83 90 86 84

75 85 77 88 85 90 85 83

83 86 83 84 86 92 85 80

76 88 79 84 80 88 80 88

1. Lengths (in centimeters) of seedlings in a plant box:

8 8.6 12 10 8 10.5 8 10.6

8.6 10.5 7.4 6.4 12.2 6.5 12 6.8

7.5 8 11 8.5 9.5 12 11.5 12.5

10.4 7 6.8 7 7 10.5 7 7

7 8.3 7 13.5 12.5 7 7 12.5 10 6.8 10.2 6 6.5 10.3 6.8 6.8

Given the population: 1, 3, 4, 6, and 8; and suppose samples of size 3 are drawn from this population:

1. What is the mean and standard deviation of the population?

2. How many different samples of size n=3 can be drawn from the population? List them with their corresponding means.

3. Construct the sampling distribution of the sample means.

4. What is the mean of the sampling distribution of the sample means? Compare this to the mean of the population.

5. What is the standard deviation of the sampling distribution of the sample means? Compare this to the standard deviation of the population.

Suppose a population consists of the five measurements: 2, 6, 8, 0, and 1:

1. What is the mean and standard deviation of the population?

2. How many different samples of size n=2 can be drawn from the population? List them with their corresponding means.

SAMPLE MEAN

3. Construct the sampling distribution of the sample means.

4. What is the mean of the sampling distribution of te sample means? Compare this to the mean of the population.

5. What is the standard deviation of the sampling distribution of the sample means? Vompare this to the standard deviation of the population.

Consider all samples of size 5 from this population:

2 5 6 8 10 12 13

1. Compute the mean and standard deviation of the population.

2. List all samples of size 5 and compute the mean for each sample.

SAMPLE MEAN

3. Construct the sampling distribution of the sample means.

4. Calculate the mean of the sampling distribution of the sample means. Compare this to the mean of the population.

5. Calculate the standard deviation of the sampling distribution of the sample means. Compare this to the standard deviation of the population.

Find the finite population correction factor given the following:

1. N=200, n=10

2. N=2000, n=10

3. N=400, n=40

4. N=500, n=10

5. N=200, n=20