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Introduction to Inference
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The distribution of the amount of money that students spend on coffee per month is right skewed with μ = $10 and σ = $125. In a SRS of 30 students, what is the probability that these students will spend on average, less than $55 on coffee?
98%
CandyCorp claims that mean Skittles consumption is 254 kcal/d with σ = 540 kcal. A sample of 150 people have a mean Skittles consumption of 369.4 kcal/d. Does this suggest greater consumption than the CandyCorp claim? (α = 0.01)
Yes, evidence supports that the true mean Skittle consumption is greater than the CandyCorp claim. p = .0044 and p ≤ α. Reject Ho. Evidence supports Ha.
The p-value for a significance test is 0.059. Do you reject the null hypothesis at level α = 0.01? Explain how you determined your answer.
No, fail to reject the null hypothesis. We fail to reject the null when the p-value is greater than alpha. We do not have evidence to support the alternative.
The p-value for a significance test is 0.033. Do you reject the null hypothesis at level α = 0.05? Explain how you determined your answer.
Yes, reject the null hypothesis. Reject the null when the p-value is less than or equal to alpha. Evidence supports the alternative hypothesis.
On average, mice complete a maze in 20 sec. Will music cause this time to differ? You measure how long each of 12 mice takes with music as a stimulus. State the null and the alternative hypothesis needed to answer this question.
Ho: μ = 20 sec., Ha: μ ≠ 20 sec.
Apartments are advertised to be 880 sqft. You and 5 of your friends think that the apartments are smaller than advertised. State the null and the alternative hypothesis needed to answer this question using the correct mathematical notation.
Ho: μ = 880 sqft., Ha: μ < 880 sqft.
The average annual amount 1593 families paid for college in 2023 was $24,164. If the population standard deviation is $8500, give the 90% confidence interval for μ, the average annual amount a family pays for college.
($23,814, $24,514)
You are planning to study the average Halloween candy consumption of Americans. With a margin of error no more than 15 kcal/d and a standard deviation equal to 540 kcal/d, what is the sample size needed for a 99% C.I.?
8600 Americans
The mean stress level of 720 millennials was found to be 5.5 (on a 10-point scale). Assume the population standard deviation is 2.8. Find the 95% confidence interval for this sample.
(5.2955, 5.7045)
Which sample will yield a confidence interval with a larger margin of error? (A) A simple random sample of 300 students at your college or university. (B) A simple random sample of 200 students at your college or university. Explain.
B) A smaller sample produces a larger confidence interval (larger m). A large sample will better estimate the mean and produce a smaller confidence interval.
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