What can be done to decrease the probabilities of committing Type1 and Type2 errors? a)decrease sample size n b) increase confidence level c) increase sample size n d) decrease confidence level
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What can be done to decrease the probabilities of committing Type1 and Type2 errors?
a)decrease
b) increase confidence level
c) increase sample size n
d) decrease confidence level
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- Cost of meals: A sample of eight dishes for a new restaurent's menu was created, and the cost of each meal (dish), in dollars is: 30 35 19 23 27 22 26 16 a) Are the assumptions for constructing a confidence interval for the mean satisfied? Explain. b) If appropriate, construct a 98% confidence interval for the mean cost of a repair.A consumer agency surveyed all 2500 families living in a small town to collect data on the number of television sets owned by them. The following table lists the frequency distribution of the data collected by this agency. 5. Number of TV sets owned 1 2 3 4 Number of families 120 970 730 410 270 (a) Construct a probability distribution table for the numbers of television sets owned by these families. Draw a bar graph of the probability distribution. Are the probabilities listed in the table of part a) exact or approximate probabilities of various outcomes? Explain. Let X denote the number of television sets owned by a randomly selected family from this town. Find the following probabilities. (i) (iii) Find the mean and standard deviation for the probability distribution developed for the number of television sets owned by all 2500 families in a town. Give a brief interpretation of the values of the mean and standard deviation. (b) (c) P(X= 1) P(X 2) P(1< X <3) (d)In a statistics activity, students are asked to determine the proportion of times that a spinning penny will land with tails up. The students are instructed to spin the penny 10 times and record the number of times the penny lands tails up. For one student, it lands tails side up six times. The student will construct a 90% confidence interval for the true proportion of tails up. Are the conditions for inference met? Yes, the conditions for inference are met. No, the 10% condition is not met. No, the randomness condition is not met. No, the Large Counts Condition is not met.
- ThanksIn a statistics activity, students are asked to determine the proportion of times that a spinning penny will land with tails up. The students are instructed to spin the penny 10 times and record the number of times the penny lands tails up. For one student, it lands tails side up six times. The student will construct a 90% confidence interval for the true proportion of tails up. Are the conditions for inference met? Yes, the conditions for inference are met. No, the 10% condition is not met. No, the randomness condition is not met. O No, the Large Counts Condition is not met.What would happen (other things being equal) to a confidence interval if you calculated a 95% confidence interval rather than a 99% confidence interval? a) It will be wider b) It will be narrower c) It will not change
- Probability of a TYPE I error in a population mean hypothesis testing can be reduced using the following methods (choose all what you think is correct) : A. Increasing sample size B. Decreasing sample size C. Decreasing significance level D. Increasing significance levelThe two main methods of statistical inference are Confidence Intervals and Hypothesis Testing. 1) TRUE 2) FALSE28. Graduation The U.S. Department of Commerce reported the results of a large-scale survey on high school graduation. Researchers contacted more than 25,000 Americans aged 24 years to see if they had finished high school; 84.9% of the 12,460 males and 88.1% of the 12,678 females indicated that they had high school diplomas. a) Are the assumptions and conditions necessary for inference satisfied? Explain. b) Create a 95% confidence interval for the difference in gradu- ation rates between males and females. c) Interpret your confidence interval. d) Does this provide strong evidence that girls are more likely than boys to complete high school? Explain.
- When we construct a confidence interval estimate of the difference between population proportions (p1-p2), if the confidence interval does not include 0, what can we conclude? a) We can conclude that p1 is significantly larger than p2. b) We can conclude that p1 is significantly smaller than p2. c) We can conclude that p1 and p2 are not significantly different O d) We can conclude that p1 and p2 are significantly different3. The Pew Research Center has conducted extensive research on the young adult population (Pew Research website, November 6, 2012). One finding was that 93% of adults aged 18 to 29 use the Internet. Another finding was that 21% of those aged 18 to 28 are married. Assume the sample size associated with both findings is 500. a) Develop a 95% confidence interval for the proportion of adults aged 18 to 29 who use the Internet. b) Develop a 99% confidence interval for the proportion of adults aged 18 to 28 who are married. c) In which case, part (a) or part (b), is the margin of error larger? Explain why.