STK110 Preparation sheet: TUT 10 memo 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 (𝑛 ) 20 15
Sample mean (𝑥̅ ) 20 18
Population variance (𝜎 ) 5.6 4.5
Let: 𝜇 population mean of the age of the females
𝜇 population mean of the age of the males
a. Formulate the hypotheses.
𝐻 :𝜇 𝜇 0
𝐻 :𝜇 𝜇 0
b. Determine the rejection rule using the 𝑝 value approach.
Reject 𝐻 if 𝑝 0.01
c. Calculate the value of the test statistic and the 𝑝 value.
𝑥̅ 𝑥̅ 𝐷 20 18 0
𝑧 2.6261 2.63
𝜎 5.6 4.5
𝜎
20 15
𝑛 𝑛
𝑝 value: 𝑝 𝑃 𝑧 2.63 1 𝑃 𝑧 2.63 1 0.9957 0.0043
d. Make a decision.
0.0043 0.01, Reject 𝐻 at a 0.01 level of significance.
e. Conclude and interpret.
At a 0.01 level of significance there is sufficient evidence to conclude that the mean age of females to
start smoking cigarettes is significantly older than men.
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)
𝑛 = 10 𝑛 = 12
𝑥̅ = 9.6 𝑥̅ = 15.6
𝑠 =9 𝑠 = 14
Given: The degrees of freedom = 18
Let: 𝜇 population mean nicotine absorption from e-cigarettes
𝜇 population mean nicotine absorption from tobacco cigarettes
a. Calculate the point estimate of 𝜇 𝜇 .
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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 (𝑛 ) 20 15
Sample mean (𝑥̅ ) 20 18
Population variance (𝜎 ) 5.6 4.5
Let: 𝜇 population mean of the age of the females
𝜇 population mean of the age of the males
a. Formulate the hypotheses.
𝐻 :𝜇 𝜇 0
𝐻 :𝜇 𝜇 0
b. Determine the rejection rule using the 𝑝 value approach.
Reject 𝐻 if 𝑝 0.01
c. Calculate the value of the test statistic and the 𝑝 value.
𝑥̅ 𝑥̅ 𝐷 20 18 0
𝑧 2.6261 2.63
𝜎 5.6 4.5
𝜎
20 15
𝑛 𝑛
𝑝 value: 𝑝 𝑃 𝑧 2.63 1 𝑃 𝑧 2.63 1 0.9957 0.0043
d. Make a decision.
0.0043 0.01, Reject 𝐻 at a 0.01 level of significance.
e. Conclude and interpret.
At a 0.01 level of significance there is sufficient evidence to conclude that the mean age of females to
start smoking cigarettes is significantly older than men.
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)
𝑛 = 10 𝑛 = 12
𝑥̅ = 9.6 𝑥̅ = 15.6
𝑠 =9 𝑠 = 14
Given: The degrees of freedom = 18
Let: 𝜇 population mean nicotine absorption from e-cigarettes
𝜇 population mean nicotine absorption from tobacco cigarettes
a. Calculate the point estimate of 𝜇 𝜇 .
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