Statistical Inference

What is the purpose of taking a sample instead of a census?

• To eliminate sampling error

• To reduce costs and time

• To collect data from every element

• To ensure perfect information about the population

What does the null hypothesis (H0) represent?

• A statement that is always true

• A conclusion drawn from the sample data

• A tentative conjecture about a population parameter

• The opposite of the alternative hypothesis

Which of the following is a characteristic of a simple random sample?

• Samples are taken from only one subgroup of the population

• Each sample of size n has the same probability of being selected

• All elements are selected based on convenience

• Each element has a different probability of being selected

What is the expected value of the sample mean (x)?

• It is always less than the population mean

• It is always equal to the population mean (m)

• It is the same as the sample standard deviation

• It can be greater than the population mean

What is the purpose of the t distribution in hypothesis testing?

• To ensure the sample size is always large

• To estimate the population mean when the standard deviation is unknown

• To provide a narrower margin of error

• To replace the need for a sample

What is the margin of error in an interval estimate?

• The value added and subtracted from the point estimate

• The range of values that the population parameter can take

• The standard deviation of the sample

• The difference between the sample mean and population mean

Which of the following conditions must be satisfied for the sampling distribution of p to be approximated by a normal distribution?

• n < 30 and p < 0.5

• np < 5 and n(1-p) < 5

• np > 5 and n(1-p) > 5

• n must be equal to the population size

What does a 95% confidence interval imply?

• The interval will always contain the population mean

• 95% of all samples will have means within the interval

• If we take many samples, 95% of the intervals will contain the population mean

• There is a 95% chance that the population mean is within the interval

What is the null hypothesis in the context of the new fuel injection system?

• H0: m > 24

• H0: m = 24

• H0: m ≠ 24

• H0: m < 24

What does a p-value indicate in hypothesis testing?

• The strength of evidence against the null hypothesis

• The probability of making a Type II error

• The probability of making a Type I error

• The sample size required for the test