12. In a random sample of 1000 homes in a certain city , it is found 220 were heated by oil. How large a sample is needed if we wish to be 99% confident that our sample proportion will be within 0.05 of the true proportion of homes in the city that are heated by oil.
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- A travel agency wants to promote pleasure trips into space and wants to know which of the two commercial companies should they promote Virgin Galactic or Blue Origin? The one preferred by the customers will be the one they decide to promote. For this reason they take a random sample of 16 potential travelers, and they ask if they would prefer Virgin Galactic or Blue Origin. Let X be the number of travelers who preferred Virgin Galactic and let p=X/16 denote the corresponding proportion. Suppose that we want to show that Virgin Galactic is preferred to Blue Origin. Please formulate the null and alternative hypotheses and calculate the rejection region. Use α=0.05 Suppose that 11 out of 16 prefer Virgin Galactic and that α = 0.05, is this enough evidence to show that Virgin Galactic is preferred to Blue Origin? Perform the test and give your conclusion. Which company should they promote?615.
- 10. Claim: P₁ = P₂; α = 0.05. Sample statistics: x1 = 265, n₁ - X2 204, 2 - 301, 247 'D11. Suppose average weight in Louisiana is 185 pounds. Suppose that John randomly selects 100 Louisianans, asks their weight, and averages the 100 numbers. Suppose that Julia does the same thing, only she asks 1,000 Louisianans instead of 100. Explain precisely, in a paragraph or so, what the Law of Large Numbers would tell you to expect about the average weights that Julia and John will calculate from their respective samples.6. A sample of 5 fathers and their eldest sons gave the following data about their weight in Kgs. Father (x): 65 60 67 63 74 Son (y): 49 45 57 40 60 CS Scanned with CamScanner
- 7. In a sample of n= 6, five individuals all have scores of X= 10 and the sixth has a score of X=16. What is the mean for this sample?2. In a population it is estimated that 20% have a desired trait of interest for the researcher. The researcher wants to know how many people on average he has to draw from a population to get 2 people with the trait. Use rows 20-24 of the Random Number Table to carry out the simulation. Explain clearly how you set up the problem and report your findings. Answer:3. At a factory that produces doorknobs, a batch of 1500 doorknobs has just been produced. To check the quality of the doorknobs, a random sample of 100 doorknobs is selected to test for defects. Out of these 100 doorknobs, 2 were found to be defective. Based on these results, what is the best estimate you can give for the number of defective doorknobs in the batch of 1500? Solve this problem in two different ways, explaining your reasoning in each case. just been
- 11. A population consists of the data (1, 2, 3, 4). 4. How many different samples of size n = 2 can be drawn from the population? a. 6 b. 5 c. 4 d. 3 For numbers 12-14, please refer to the problem below. A population consists of five (5) measurements 2, 3, 6, 5, and 7. 12. How many different samples of size n = 2 can be drawn from the population? a. 7 b. 8 c. 9 d. 10 13. What is the mean of the sampling distribution of the sample means? a. 3.44 b. 4.60 c. 4.92 d. 5.20 14. What is the variance of the sampling distribution of the sample means with a sample size of 2? a. 0.89 b. 1.29 c. 2.20 d. 3.90 For numbers 15-16, identify whether the given situation illustrates a sampling distribution from a normal population with a) Known or b) Unknown Variance 15. IQ scores are normally distributed with standard deviation o= 15 points. You wish to determine the mean IQ of all students in Matiyaga National High School by taking a random sample of 16 students. 16. The general weighted average (GWA)…32)1.3 of your textbook about the automobile that was tested for production defects, but assume that the number of production defects is 21 and that 12 of these are classified as major defects, 11 are classified as design defects, and 6 were neither major defects nor design defects. How many of the design defects were major?