Formative questions week 3
1. Given: Suppose a sample of 81 youngsters between 16 and 25 years old is drawn. The
average alcohol consumption per week turns out to be 5.4 glasses of beer. The standard
deviation of alcohol consumption in the sample of youngsters is 4.1.
Question: We test the following hypotheses: H0: μ = 4 glasses versus Ha: μ ≠ 4 glasses.
What is the value of the t-test?
a) t = (5.4 – 4)/ (4.1/√81)
b) t = (5.4 – 4)/ (4.1)
c) t = (5.4 – 4)/ (4.1)2
d) t = (5.4 – 4)/ (4.1/√81)2
2. Given: A sample of 110 adults between 30 and 50 years. The average alcohol consumption
turns out to be 3.4 glasses of beer per week. We test the following hypotheses: H0: μ = 4
glasses versus Ha: μ ≠ 4 glasses. We find as value for the t-test: t = - 1.85, with p-value =
0.067. A significance level of α = 0.05 is being used.
Question: Which statement is correct ?
a) The value 4 is outside the 95% confidence interval for the population mean
b) The value 4 is inside the 95% confidence interval for the population mean
c) The value 4 is exactly on one of the borders of the 95% confidence interval for the
population mean
3. Given: See Problem 2. Question: In which of the situations below does the researcher make
a type II error?
a) The null hypothesis is rejected, while the average alcohol consumption in the population
is equal to 5.
b) The null hypothesis is rejected, while the average alcohol consumption in the population
is equal to 4
c) The null hypothesis is accepted, while the average alcohol consumption in the population
is equal to 5
d) The null hypothesis is accepted, while the average alcohol consumption in the population
is equal to 4.
4. Given: The following two statements:
A. If the p-value of a t-test is larger than the significance level, researchers denote
this as a significant result.
B. The p-value can be interpreted as the probability that the null hypothesis is true.
Question: Which of the statements is true ?
a) Statement A is true and statement B is true
b) Statement A is false and statement B is true
c) Statement A is true and statement B is false
d) Statement A is false and statement B is false
1. Given: Suppose a sample of 81 youngsters between 16 and 25 years old is drawn. The
average alcohol consumption per week turns out to be 5.4 glasses of beer. The standard
deviation of alcohol consumption in the sample of youngsters is 4.1.
Question: We test the following hypotheses: H0: μ = 4 glasses versus Ha: μ ≠ 4 glasses.
What is the value of the t-test?
a) t = (5.4 – 4)/ (4.1/√81)
b) t = (5.4 – 4)/ (4.1)
c) t = (5.4 – 4)/ (4.1)2
d) t = (5.4 – 4)/ (4.1/√81)2
2. Given: A sample of 110 adults between 30 and 50 years. The average alcohol consumption
turns out to be 3.4 glasses of beer per week. We test the following hypotheses: H0: μ = 4
glasses versus Ha: μ ≠ 4 glasses. We find as value for the t-test: t = - 1.85, with p-value =
0.067. A significance level of α = 0.05 is being used.
Question: Which statement is correct ?
a) The value 4 is outside the 95% confidence interval for the population mean
b) The value 4 is inside the 95% confidence interval for the population mean
c) The value 4 is exactly on one of the borders of the 95% confidence interval for the
population mean
3. Given: See Problem 2. Question: In which of the situations below does the researcher make
a type II error?
a) The null hypothesis is rejected, while the average alcohol consumption in the population
is equal to 5.
b) The null hypothesis is rejected, while the average alcohol consumption in the population
is equal to 4
c) The null hypothesis is accepted, while the average alcohol consumption in the population
is equal to 5
d) The null hypothesis is accepted, while the average alcohol consumption in the population
is equal to 4.
4. Given: The following two statements:
A. If the p-value of a t-test is larger than the significance level, researchers denote
this as a significant result.
B. The p-value can be interpreted as the probability that the null hypothesis is true.
Question: Which of the statements is true ?
a) Statement A is true and statement B is true
b) Statement A is false and statement B is true
c) Statement A is true and statement B is false
d) Statement A is false and statement B is false
