A 5-point Likert question yielded the following counts: 10 respondents chose 1, 20 chose 2, 40 chose 3, 50 chose 4, and 30 chose 5.
Compute the sample mean and sample standard deviation.
[4]The following table shows the frequency of responses on a 5-point Likert scale, where 1 represents "Strongly Disagree" and 5 represents "Strongly Agree".
| Score () | 1 | 2 | 3 | 4 | 5 |
|---|---|---|---|---|---|
| Frequency () | 10 | 20 | 40 | 50 | 30 |
Convert the scores to a percentage scale where 1 maps to and 5 maps to . Calculate the mean percentage for the responses.
[3]Two survey question wordings yield these results: Sample A (biased wording): 80 out of 150 “yes”; Sample B (neutral wording): 60 out of 150 “yes”. Test at the 5% level whether the proportions differ significantly.
[6]Sample size calculation for comparing two proportions using the standard formula for power and significance.
Compute the required sample size per group to detect a difference between two proportions and with 80% power at a 5% significance level (two-sided).
[5]In a survey of 250 respondents to a closed yes/no question, 175 answered “yes”. Calculate the sample proportion of “yes” responses and the variance of .
[3]This question assesses the ability to determine the minimum sample size required for estimating a population proportion with a specific margin of error and confidence level.
Determine the minimum sample size required to estimate a population proportion within a margin of error of at confidence, assuming a conservative estimate .
[4]A finite population of size has a true proportion . A simple random sample of size is drawn without replacement. Calculate the variance of the sample proportion using the finite population correction.
[3]A survey of a population with a sample size of resulted in a sample proportion of .
Find a 95% confidence interval for the population proportion .
[4]Statistics - Discrete random variables - Discrete uniform distribution properties.
A survey uses a question on a 4-point scale from “Strongly Disagree” to “Strongly Agree”. If the true underlying opinions follow a discrete uniform distribution over the set , calculate the mean and variance of the ratings.
[4]A poorly worded survey question yielded 70% “agree” from 400 respondents. After rewriting to remove bias, only 52% agreed out of another 400 respondents. Calculate the absolute and relative change in agreement rate.
[4]In a random sample of 5 survey respondents from a large population where the true “yes” probability is 0.6, what is the probability exactly 3 answer “yes”?
[3]