PSYCH 240 HW4 Page 1 unit 4: foundations of statistical inference This homework assignment focuses on samples, sampling distributions, and confidence intervals. For all questions, round to three decimal places while working and two decimal places for your final answer. 1. In your own words, describe the difference between a sampling distribution and a distribution of data. 2. The standard deviation of a sampling distribution is called the _______________________ and the mean is called the _______________________. 3. Calculate the standard error (𝜎x) using the information provided in the questions below. a. 𝜎 = 14.2, N = 40 b. 𝜎 = 3.43, N = 30 c. 𝜎 = 154, N = 50 d. 𝜎 = 7.4, N = 16 e. 𝜎 = 14.38, N = 100 TextPSYCH 240 HW4 Page 2 4. Describe the Central Limit Theorem in your own words. 5. How is the normal distribution related to t-distributions? 6. For IQ, μ = 100 and 𝜎 = 15. Based on this information, answer the following questions. a. What is the probability that a first-grade classroom of 25 students who are chosen randomly from the population will have a mean IQ of 105 or greater? b. What is the probability that a first-grade classroom of 25 students who are chosen randomly from the population will have a mean IQ of 90 or less? 7. Fill in the blanks with either: t or normal. a. There is just one ___________ distribution, but there are many ___________ distributions. b. Given a value of +2.00 on the horizontal axis, a ___________ has a greater proportion to the right than does a ___________ distribution. c. The ___________ distribution has a larger standard deviation than does the ___________ distribution. 8. To know which t distribution to use, we must first determine: a. Standard deviation b. Standard error of the mean c. Mean d. Degrees of freedomPSYCH 240 HW4 Page 3 9. Airplane manufacturers prefer to use slow-burning materials. The plastic in coffee pots used on airplanes has a maximum burn rate of 4 inches per minute. An engineer randomly sampled 3 Krups coffee pots (N = 3) from a case of 120 pots. He obtained an average burn rate of 1.20 inches per minute. Can the engineer conclude that the case of Krups coffee pots meet burn rate specifications? a. Given 𝑠#= 0.10(inches, compute 𝑠!". b. Compute degrees of freedom and find a t-value (α = .001). c. Compute a confidence interval. d. Write a conclusion.PSYCH 240 HW4 Page 4 10. We consider normal human body temperature to be 98.6°F (Farenheit). However, one study by Mackowiak et al. (1992) found that the average human body temperature in their sample (N = 40) was less than 98.6°F. (𝑥0 = 98.2°F). Is their sample mean within the expected range of sample means taken from a population with a mean of 98.6°F? Or have we been wrong all these years? a. Given 𝑠#= 0.710, compute 𝑠!". b. Compute degrees of freedom and find a t-value (α = .01). c. Compute a confidence interval. d. Write a conclusion.