Question

apply statistical methods and analysis. Unless otherwise stated, use 5% (.05) as your alpha level (cutoff for statistical significance).


#1.  For each example, state whether the one-sample, two-independent-sample, or related-samples t test is most appropriate. If it is a related-samples t test, indicate whether the test is a repeated-measures design or a matched-pairs design.     

A professor tests whether students sitting in the front row score higher on an exam than students sitting in the back row.

A graduate student selects a sample of 25 participants to test whether the average time students attend to a task is greater than 30 minutes.

A researcher matches right-handed and left-handed siblings to test whether right-handed siblings express greater emotional intelligence than left-handed siblings.

A principal at a local school wants to know how much students gain from being in an honors class. He gives students in an honors English class a test prior to the school year and again at the end of the school year to measure how much students learned during the year.

#2.

A random sample of 25 professional basketball players shows a mean height of 6 feet, 5 inches with a 95% confidence interval of 0.4 inches. Explain what this indicates.

If the sample were smaller, would the confidence interval become smaller or larger? Explain.

If you wanted a higher level of confidence (99%) would the confidence interval become smaller or larger? Explain.

Answer 1

#1

A professor tests whether students sitting in the front row score higher on an exam than students sitting in the back row.

Here, the two different samples are tested independent of each other and compared hence, it is two-independent-sample t test.

A graduate student selects a sample of 25 participants to test whether the average time students attend to a task is greater than 30 minutes.

Here, only one samples is tested for the average time students attend to a task hence, it is one-sample t test.

A researcher matches right-handed and left-handed siblings to test whether right-handed siblings express greater emotional intelligence than left-handed siblings.

Here, the two different samples are tested related to each other and compared hence, it is related-sample t test. Also, the matches are already made hence, it is matched-pairs design.

A principal at a local school wants to know how much students gain from being in an honors class. He gives students in an honors English class a test prior to the school year and again at the end of the school year to measure how much students learned during the year.

Here, the two different samples are tested related to each other and compared hence, it is related-sample t test. Also, the same sample is tested twice hence, it is repeated-measures design.

#2

sample size, n = 25

mean height = 6 feet, 5 inches

95% confidence interval = 0.4 inches

This mean we are 95% sure that the mean lies within 0.4 range of error from the mean of the height.

If the sample were smaller, would the confidence interval become smaller or larger?

If the sample size increases the margin of error = SE(height)*z_critical/sqrt(n) will reduce.

The margin of error will decrease.

Hence, the confidence interval will decrease.

If you wanted a higher level of confidence (99%) would the confidence interval become smaller or larger?

If the level of confidence (99%) increases the margin of error = SE(height)*z_critical/sqrt(n) will increase because z_critical will increase.

Hence, the confidence interval will increase.