Confidence Intervals and Proportions

A study found that in a sample of 44 subjects, 9 of agree that children under 6 shouldn’t be taken to nice restaurants.

The 95% confidence interval for p is (0.082, 0.318). Interpret this interval.

• 95% of the time the proportion of people who believe children under 6 shouldn't be taken to nice restaurants will be between 8.2% and 31.8%.

• The population proportion of people who believe children under 6 shouldn't be taken to nice restaurants is between 8.2% and 31.8%.

• The probability that the proportion of people who believe children under 6 shouldn't be taken to nice restaurants will be between 8.2% and 31.8% is 95%.

• I am 95% confident that the true proportion of people who believe children under 6 shouldn't be taken to nice restaurants is between 8.2% and 31.8%.

The symbol for the sample proportion is __________.

• Z_c
• p̂
• E
• q

Does the interval (3, 14) support the claim that the mean of a data set is 2.9

• Yes

• No

• Not enough information.

What is the format for interpreting a confidence interval? 

• The interval from ___ to ___ captures the true mean in context.
• C% of samples of the same size taken from the same population will capture the parameter in question
• There is convincing evidence that C% gives the interval (___, ___) capturing the parameter in question.
• We are C% confident that the interval from ___ to ___ captures the [parameter in context].

If the 95% Confidence Interval for a population mean is (114.56, 125.54), then is it likely that the true population mean µ is greater than 130?

• Yes

• No

• Not enough information

• I have no idea what you're asking of me

Which of the following changes to a study would result in a narrower confidence interval?

• increasing the confidence level, increasing the sample size
• decreasing the confidence level, decreasing the sample size
• increasing the confidence level, decreasing the sample size
• decreasing the confidence level, increasing the sample size.

What is the critical value z_c for a 99% confidence interval?

• 1.960

• 2.576

• 2.575

• 3.291

What is p-hat (sample proportion) if 53 out of 100 students possess a pencil?

• 0.45

• 0.53

• 0.60

• 0.50

What is the point estimate, p̂, for a 95% confidence interval of (0.202, 0.482)?

• 0.342

• 0.300

• 0.400

• 0.250

What is the relationship between sample size and margin of error in estimating a population proportion?

• Larger sample sizes result in a smaller margin of error.

• Larger sample sizes result in a larger margin of error.

• Sample size has no effect on margin of error.

• Smaller sample sizes result in a smaller margin of error.