Statistical Hypothesis Testing and Confidence Intervals: A Comprehensive Analysis
Analyzes hypothesis testing and confidence intervals.
Olivia Smith
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Statistical Hypothesis Testing and Confidence Intervals: A Comprehensive
Analysis
• Make sure your answers are as complete as possible and show your work/argument.
When there are calculations involved, you should show how you come up with your
answers with critical work and/or necessary tables. You must show why you choose
certain answer for true-or-false and multiple choice questions. Answers that come
straight from program software packages will not be accepted.
1. (2 pts) True or False: In a right-tailed test, the test statistic is 1.5. If we know P(X < 1.5) =
0.96, then we reject the null hypothesis at 0.05 level of significance. (Justify for full credit)
Because
P(X
2. (2 pts) True or False: If a 99% confidence interval contains 1, thenthe 95% confidence interval
for the same parameter must contain 1. (Justify for full credit)
Because 99% confidence is wider than 95% confidence interval so 99% confidence interval
contains 1 but 95% confidence interval may not contain 1 for the same parameter.
3. (2 pts) Which of the following could reduce the rate of Type I error? (Justify for full credit)
a. Making the significant level from 0.01 to 0.05
b. Making the significant level from 0.05 to 0.01
c. Increase the β level
d. Increase the power
Because level of significance is actually the type I error in testing of hypothesis so we need to
reduce the level of significance from 0.05 to 0.01 to reduce the type I error.
4. (2 pts) Three hundred students took a chemistry test. You sampled 50 students to estimate the
average score and the standard deviation. How many degrees of freedom were there in the
estimation of the standard deviation? (Justify for full credit)
a. 50
b. 49
c. 300
d. 299
Here the sample size n=50 so the degree of freedom is =50-1=49.
(For Questions 5&6) Mimi was the 5th seed in 2015 UMUC Tennis Open that took place in
August. In this tournament, she won 75 of her 100 serving games.
Statistical Hypothesis Testing and Confidence Intervals: A Comprehensive
Analysis
• Make sure your answers are as complete as possible and show your work/argument.
When there are calculations involved, you should show how you come up with your
answers with critical work and/or necessary tables. You must show why you choose
certain answer for true-or-false and multiple choice questions. Answers that come
straight from program software packages will not be accepted.
1. (2 pts) True or False: In a right-tailed test, the test statistic is 1.5. If we know P(X < 1.5) =
0.96, then we reject the null hypothesis at 0.05 level of significance. (Justify for full credit)
Because
P(X
2. (2 pts) True or False: If a 99% confidence interval contains 1, thenthe 95% confidence interval
for the same parameter must contain 1. (Justify for full credit)
Because 99% confidence is wider than 95% confidence interval so 99% confidence interval
contains 1 but 95% confidence interval may not contain 1 for the same parameter.
3. (2 pts) Which of the following could reduce the rate of Type I error? (Justify for full credit)
a. Making the significant level from 0.01 to 0.05
b. Making the significant level from 0.05 to 0.01
c. Increase the β level
d. Increase the power
Because level of significance is actually the type I error in testing of hypothesis so we need to
reduce the level of significance from 0.05 to 0.01 to reduce the type I error.
4. (2 pts) Three hundred students took a chemistry test. You sampled 50 students to estimate the
average score and the standard deviation. How many degrees of freedom were there in the
estimation of the standard deviation? (Justify for full credit)
a. 50
b. 49
c. 300
d. 299
Here the sample size n=50 so the degree of freedom is =50-1=49.
(For Questions 5&6) Mimi was the 5th seed in 2015 UMUC Tennis Open that took place in
August. In this tournament, she won 75 of her 100 serving games.
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Subject
Statistics