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Question 1 of 10
A researcher is conducting quality assurances on a batch of products. To estimate what proportion is defective, the researcher wants to make a one-sample z interval with 99% confidence $(z* = 2.58)$. The margin of error should be no more than 2%. A previous sample suggested 5% of the products are defective. What is the smallest sample size required to fit these parameters?
Question 2 of 10
Which of the following statements are true about the relationship between sample size, width of confidence interval, confidence level, and margin of error for a population proportion?
I. The width of the confidence interval increases as the sample size increases
II.The width of the confidence interval increases as the confidence level increases
III.The width of the confidence interval decreases as the margin of error increases
IV.The width of the confidence interval is twice the margin of error
Question 3 of 10
A teacher is trying to improve student mastery using a new teaching method. The current student mastery is 60%. The teacher does a random sample under the new teaching method and observes a new mean student mastery is 75%. What are appropriate hypotheses for the significance test?
Question 4 of 10
A student reads a newspaper article that estimates that 60% of students from the local high school attend a four-year college. The student is curious about that number and conducts a separate random sample to survey students. In the random sample of 80 students, 56 reported they were attending a four-year college. Calculate the test statistic for this population proportion.
Question 5 of 10
A medical researcher is testing the null hypothesis that a new treatment is no more effective than a previous treatment for a certain disease. What would be a Type I error in this situation?
Question 6 of 10
Assuming no other factors are changed, changing which factor can reduce the probability of a Type II error?
Question 7 of 10
The student council is investigating whether or not students support the new classroom design proposed at their high school. They are curious about the difference of opinion between older (11th and 12th grade) and younger (9th and 10th grade) students. They conduct a random survey of students from each group. Here are the results:
Support new design?
9th/10th
11th/12th
Yes
72
84
No
28
36
Total
100
120
The student council wants to use these results to construct a 95% confidence interval $(z* = 2.58)$ to estimate the difference between the proportions of students in these two groups who support the construction project. Assume all conditions for inference have been met. What is a correct 95% confidence interval based on this data?
Question 8 of 10
Which of the following could be appropriate null and alternative hypotheses for a difference of population proportions?
I. $H_0:p_1=p_2$
II. $H_0:p_1=p_2$
III. $H_0:p_1 > p_2$
IV. $H_0:p_1>p_2$
Question 9 of 10
Which of the following needs to be true when getting a confidence interval for a proportion?
Question 10 of 10
A principal wants to gather evidence for the efficacy of a mandated tutoring program. To do this, a random sample of students is taken from those in the voluntary tutoring program, and those not in the program. In the voluntary tutoring program, 75% of students are passing all of their classes. For those not in the program, 65% are passing all classes. The principal performs a significance test on the difference of proportions and the p-value returned is 0.05.
What conclusion should be drawn for a 95% level of confidence?
Current
Correct
Incorrect
