QUESTION 1
A random sample of 50 households was selected for a telephone survey. The question asked was,
”Do you or any member of your household own a cellular telephone with a built–in camera?” of the
50 respondents, 15 said yes, and 35 said no.
The standard error of households with cellular telephones with built–in camera is
(1) 0.3
(2) 0.0042
(3) 0.0648
(4) 0.7
(5) 0.1684
QUESTION 2
Given a normal population with a mean of 50 and a standard deviation of 5. Calculate the probability
that a random sample of 25 has a mean greater than 52.
(1) 0.9772
(2) 0.9778
(3) 0.0228
(4) 0.0222
(5) 0.2280
QUESTION 3
A random sample of size n = 400 was selected from a binomial population with population propor-
tion π = 0.2.
The number of observed successes in the sample is 96.
(a) Based on the outcome of the sample, what is the value of p?
(b) What is the standard error of p?
(c) Calculate P( p ≥ 0.24).
2
,QUESTION 4
When constructing a confidence interval, the t –student distribution is used when
(1) the sample size is provided
(2) the population variance is given
(3) the sample variance is given
(4) the question is to calculate the 95% confidence interval of the mean
(5) the level of significance is 1%, 5% or 10%.
QUESTION 5
The mean X¯ = 10 for a sample of 100 and the population standard deviation found as 1. The lower
limit of the 95% confidence for the population mean estimate is
(1) 0.196
(2) 10.196
(3) 9.804
(4) 10.1645
(5) 0.0196
QUESTION 6
The Sugar Producers Association wants to estimate the mean yearly sugar consumption. A sample
of 16 people reveals the mean yearly consumption to be 27.24 kilogram with a standard deviation
of 9.08 kilogram. Calculate the 90% confidence interval for the population mean.
(1) (22.551; 31.450)
(2) (25.719; 28.561)
(3) (23.261; 31.219)
(4) (22.403; 32.077)
(5) (23.021; 30.980)
3
,QUESTION 7
A survey of a random sample of 300 grocery shoppers in Kimberly found that the mean value
of their grocery purchases was R78. Assume that the population standard deviation of grocery
purchase values is R21. The 95% confidence limit for grocery purchase is
(1) (80.38 ; 75.62)
(2) (75.62 ; 80.38)
(3) (76.01 ; 79.99)
(4) (74.87 ; 81.13)
(5) (78; 2.376)
QUESTION 8
In a random sample of 500 observations, we found the proportion of successes to be 48%. The
upper limit at 95% confidence interval estimate for population proportion of successes is
(1) 0.0223
(2) 0.0438
(3) 0.5238
(4) 0.4362
(5) 0.5167
QUESTION 9
Given the following information:
H0 : µ = 50 against H1 : µ /= 50
σ = 15 n = 100 X¯ = 48, a = 0.05
Which one of the following statements is correct?
(1) A one–tail test is used.
(2) A standard deviation of the mean is 0.15.
(3) The test statistic is 1.33.
(4) The critical value is 1.645.
(5) The p–value is 0.1836.
4
, QUESTION 10
A statistics practitioner formulated the following hypothesis:
H0 : µ = 200 versus H1 : µ < 200 X¯ = 190, n = 9, S = 50
Which one of the following statements is incorrect?
(1) A one–tail test is advisable to be used.
(2) The t –student test statistic is used.
(3) The test statistic is t = —0.6.
(4) The critical value at a = 0.01 is 2.821
(5) Fail to reject H0 at 1% level of significance.
QUESTION 11
A statistics practitioner wants to test the following hypotheses:
H0 : π = 0.70
H1 : π /= 0.70
A random sample of 100 produced p = 0.73 and the statistic z = 0.65, then, the p–value is
(1) 0.03
(2) 0.2578
(3) 0.0458
(4) 0.6546
(5) 0.5156
QUESTION 12
An airline claims that only 6% of all lost luggage is never found. If in a random sample, 17 of
200 pieces of lost luggage are not found, test the null hypothesis π= 0.06 against the alternative
hypothesis π > 0.06. Which one of the following statements is incorrect ?
(1) p = 0.085
(2) The standard error is 0.01679
(3) The test statistic is equal to 1.49
(4) The p-value is 0.0681
(5) The null hypothesis is not rejected at the 0.10 level of significance.
5
A random sample of 50 households was selected for a telephone survey. The question asked was,
”Do you or any member of your household own a cellular telephone with a built–in camera?” of the
50 respondents, 15 said yes, and 35 said no.
The standard error of households with cellular telephones with built–in camera is
(1) 0.3
(2) 0.0042
(3) 0.0648
(4) 0.7
(5) 0.1684
QUESTION 2
Given a normal population with a mean of 50 and a standard deviation of 5. Calculate the probability
that a random sample of 25 has a mean greater than 52.
(1) 0.9772
(2) 0.9778
(3) 0.0228
(4) 0.0222
(5) 0.2280
QUESTION 3
A random sample of size n = 400 was selected from a binomial population with population propor-
tion π = 0.2.
The number of observed successes in the sample is 96.
(a) Based on the outcome of the sample, what is the value of p?
(b) What is the standard error of p?
(c) Calculate P( p ≥ 0.24).
2
,QUESTION 4
When constructing a confidence interval, the t –student distribution is used when
(1) the sample size is provided
(2) the population variance is given
(3) the sample variance is given
(4) the question is to calculate the 95% confidence interval of the mean
(5) the level of significance is 1%, 5% or 10%.
QUESTION 5
The mean X¯ = 10 for a sample of 100 and the population standard deviation found as 1. The lower
limit of the 95% confidence for the population mean estimate is
(1) 0.196
(2) 10.196
(3) 9.804
(4) 10.1645
(5) 0.0196
QUESTION 6
The Sugar Producers Association wants to estimate the mean yearly sugar consumption. A sample
of 16 people reveals the mean yearly consumption to be 27.24 kilogram with a standard deviation
of 9.08 kilogram. Calculate the 90% confidence interval for the population mean.
(1) (22.551; 31.450)
(2) (25.719; 28.561)
(3) (23.261; 31.219)
(4) (22.403; 32.077)
(5) (23.021; 30.980)
3
,QUESTION 7
A survey of a random sample of 300 grocery shoppers in Kimberly found that the mean value
of their grocery purchases was R78. Assume that the population standard deviation of grocery
purchase values is R21. The 95% confidence limit for grocery purchase is
(1) (80.38 ; 75.62)
(2) (75.62 ; 80.38)
(3) (76.01 ; 79.99)
(4) (74.87 ; 81.13)
(5) (78; 2.376)
QUESTION 8
In a random sample of 500 observations, we found the proportion of successes to be 48%. The
upper limit at 95% confidence interval estimate for population proportion of successes is
(1) 0.0223
(2) 0.0438
(3) 0.5238
(4) 0.4362
(5) 0.5167
QUESTION 9
Given the following information:
H0 : µ = 50 against H1 : µ /= 50
σ = 15 n = 100 X¯ = 48, a = 0.05
Which one of the following statements is correct?
(1) A one–tail test is used.
(2) A standard deviation of the mean is 0.15.
(3) The test statistic is 1.33.
(4) The critical value is 1.645.
(5) The p–value is 0.1836.
4
, QUESTION 10
A statistics practitioner formulated the following hypothesis:
H0 : µ = 200 versus H1 : µ < 200 X¯ = 190, n = 9, S = 50
Which one of the following statements is incorrect?
(1) A one–tail test is advisable to be used.
(2) The t –student test statistic is used.
(3) The test statistic is t = —0.6.
(4) The critical value at a = 0.01 is 2.821
(5) Fail to reject H0 at 1% level of significance.
QUESTION 11
A statistics practitioner wants to test the following hypotheses:
H0 : π = 0.70
H1 : π /= 0.70
A random sample of 100 produced p = 0.73 and the statistic z = 0.65, then, the p–value is
(1) 0.03
(2) 0.2578
(3) 0.0458
(4) 0.6546
(5) 0.5156
QUESTION 12
An airline claims that only 6% of all lost luggage is never found. If in a random sample, 17 of
200 pieces of lost luggage are not found, test the null hypothesis π= 0.06 against the alternative
hypothesis π > 0.06. Which one of the following statements is incorrect ?
(1) p = 0.085
(2) The standard error is 0.01679
(3) The test statistic is equal to 1.49
(4) The p-value is 0.0681
(5) The null hypothesis is not rejected at the 0.10 level of significance.
5
