STK110 Preparation sheet: TUT 10 2023
Question 1
A researcher would like to investigate whether females start smoking cigarettes at an older age than males.
A total of 20 females and 15 males are selected randomly from normal populations and the descriptive
statistics for the age of the respondents are tabulated below. Use α = 0. 01
Females (Population 1) Males (Population 2)
Sample size (𝑛𝑖) 20 15
Sample mean (𝑥𝑖) 20 18
Population variance (σ𝑖 )
2 5.6 4.5
Let: µ1 = population mean of the age of the females
µ2 = population mean of the age of the males
a. Formulate the hypotheses.
b. Determine the rejection rule using the 𝑝 −value approach.
c. Calculate the value of the test statistic and the 𝑝 −value.
d. Make a decision.
e. Conclude and interpret.
Question 2
A researcher wants to test whether there is a difference between the mean nicotine absorption from
e-cigarettes and tobacco cigarettes. He has drawn two independent random samples from populations that
are normally distributed and used a significance level of α = 0. 05.
The nicotine absorption (ng/ml) from e-cigarettes and tobacco cigarettes are noted and the following
statistics calculated:
e-cigarettes (Population 1) tobacco cigarettes (Population 2)
𝑛1 = 10 𝑛2 = 12
𝑥1 = 9.6 𝑥2 = 15.6
𝑠1 = 9 𝑠2 = 14
Given: The degrees of freedom = 18
Let: µ1 = population mean nicotine absorption from e-cigarettes
µ2 = population mean nicotine absorption from tobacco cigarettes
a. Calculate the point estimate of µ1 − µ2.
b. Determine the value of the standard error of 𝑥1 − 𝑥2
c. Formulate the hypotheses.
d. Determine the rejection rule using the critical value approach.
e. Calculate the value of the test statistic.
f. Make a decision.
g. Conclude and interpret.
h. If 𝐻0 is wrongly rejected in step f, the error that is made, is a:
i. Compute a 95% confidence interval for the population mean. Does it support your conclusion in g?
j. Calculate the 𝑝-value.
Preliminary solutions:
Question 1 Question 2
a. 𝐻0: ; 𝐻𝑎: a. -6
b. 𝑝≤ b. 4. 943
Question 1
A researcher would like to investigate whether females start smoking cigarettes at an older age than males.
A total of 20 females and 15 males are selected randomly from normal populations and the descriptive
statistics for the age of the respondents are tabulated below. Use α = 0. 01
Females (Population 1) Males (Population 2)
Sample size (𝑛𝑖) 20 15
Sample mean (𝑥𝑖) 20 18
Population variance (σ𝑖 )
2 5.6 4.5
Let: µ1 = population mean of the age of the females
µ2 = population mean of the age of the males
a. Formulate the hypotheses.
b. Determine the rejection rule using the 𝑝 −value approach.
c. Calculate the value of the test statistic and the 𝑝 −value.
d. Make a decision.
e. Conclude and interpret.
Question 2
A researcher wants to test whether there is a difference between the mean nicotine absorption from
e-cigarettes and tobacco cigarettes. He has drawn two independent random samples from populations that
are normally distributed and used a significance level of α = 0. 05.
The nicotine absorption (ng/ml) from e-cigarettes and tobacco cigarettes are noted and the following
statistics calculated:
e-cigarettes (Population 1) tobacco cigarettes (Population 2)
𝑛1 = 10 𝑛2 = 12
𝑥1 = 9.6 𝑥2 = 15.6
𝑠1 = 9 𝑠2 = 14
Given: The degrees of freedom = 18
Let: µ1 = population mean nicotine absorption from e-cigarettes
µ2 = population mean nicotine absorption from tobacco cigarettes
a. Calculate the point estimate of µ1 − µ2.
b. Determine the value of the standard error of 𝑥1 − 𝑥2
c. Formulate the hypotheses.
d. Determine the rejection rule using the critical value approach.
e. Calculate the value of the test statistic.
f. Make a decision.
g. Conclude and interpret.
h. If 𝐻0 is wrongly rejected in step f, the error that is made, is a:
i. Compute a 95% confidence interval for the population mean. Does it support your conclusion in g?
j. Calculate the 𝑝-value.
Preliminary solutions:
Question 1 Question 2
a. 𝐻0: ; 𝐻𝑎: a. -6
b. 𝑝≤ b. 4. 943
