In six packages of "The Flintstones® Real Fruit Snacks" there were eight Bam-Bam snack pieces. The total number of snack pieces in the six bags was 67. We wish to calculate a 96% confidence interval for the population proportion of Bam-Bam snack pieces. Part (a) Define the random variables X and P' in words. X is the number of Bam-Bam snacks in a sample of 67 snack pieces. P' is the proportion of Bam-Bam pieces in a bag of snacks.X is the proportion of Bam-Bam snacks in a bag of snacks. P' is the proportion of Bam-Bam pieces in a sample of 67 snack pieces.    X is the proportion of Bam-Bam snacks in a sample of 67 snack pieces. P' is the proportion of Bam-Bam pieces in a bag of snacks.X is the number of Bam-Bam snacks in a bag of snacks. P' is the number of Bam-Bam pieces in a sample of 67 snack pieces. Part (b) Which distribution should you use for this problem? (Enter your answer in the form z or tdf where df is the degrees of freedom.)       Explain your choice. The binomial distribution should be used because the two outcomes are "Bam-Bam" and "Not Bam-Bam".The Student's t-distribution should be used because    npq ≤ 10,  which implies a small sample.    The Student's t-distribution should be used because we do not know the standard deviation.The standard normal distribution should be used because we are interested in proportions. Part (c) Calculate p'. (Round your answer to three decimal places.) p' =  Part (d) Construct a 96% confidence interval for the population proportion of Bam-Bam snack pieces per bag. (Round your answers to three decimal places.) (i) State the confidence interval.

A union of restaurant and foodservice workers would like to estimate this year's mean hourly wage, u, of foodservice workers in the U.S. Last year's mean hourly wage was $8.08, and there is reason to believe that this year's value is different from last year's. The union decides to do a statistical test to see if the value has indeed changed. The union chooses a random sample of this year's wages, computes the mean of the sample to be $8.48, and computes the standard deviation of the sample to be $1.25. Based on this information, answer the questions below. What are the null hypothesis (H) and the alternative hypothesis (H,) that should be used for the test? H: u is [? |H: u is ? ? In the context of this test, what is a Type II error? A Type II error is ? v the hypothesis that u is ? when, in fact, u is ? Suppose that the union decides to reject the null hypothesis. What sort of error might it be making? ?

Suppose a test is given to 20 randomly selected college freshmen in Ohio. The sample average score on the test is 12 points and the sample standard deviation is 4 points. Suppose the same test is given to 16 randomly selected college freshmen in Iowa. The sample average score on the test is 8 points and the sample standard deviation is 3 points. We want to test whether there is a significant difference in scores of college freshmen in Ohio versus Iowa. Does the 90% confidence interval indicate that there is evidence of a difference in population means? Group of answer choices Yes Not enough information No

Suppose in one season, one baseball team averaged 20 run per game ( team 1), and team 2 averaged 10 runs .   Assume each team had 10 hitters (n=10 for both).  Assume that we don’t know the population standard deviations on each teams hits, but assume the sample standard deviations are 5 for each team.  Test whether this difference is significant at the 95% confidence level, i.e., it is rarely likely to occur by chance if one team isn’t really better than the other.  Use this information to answer questions 8 -12 below (Hint: Solve like “Are Men and Women Equal Talkers” Problems) The appropriate test statistic for testing whether the difference between these two means is unlikely to have happened by chance is the   z-statistic b .t-statistic chi-square statistic F-statistic   The value of the test statistic is (assume population standard deviations are unknown, and not equal).   14.14 .401 .600 4.46     At the 95% confidence level, can we say this is a common difference in…

In a sample of 10 randomly selected black bears from northeast Pennsylvania, the sample mean was 214.1 pounds and the sample standard deviation was 51.1 pounds. Construct a 99% confidence interval estimate for the population standard deviation of all black bears in this region.

A survey will be conducted to compare the grade point averages of US high-school students from four different school districts. Students are to be randomly selected from each of the four districts and their grade point averages recorded. The ANOVA model most likely to fit this situation is: O oneway ANOVA based on independent samples. O two-way ANOVA based on independent samples. O one-way ANOVA based on randomised blocks. O random effects ANOVA

A telephone poll of 500 adult Americans was reported in an issue of Time Magazine.  One of the questions asked was “What is the main problem facing the country?”   Thirty percent answered “crime”.  We are interested in the population proportion of adult Americans who feel that crime is the main problem. Define the random variables X and P’ in words. Which distribution should be used for this problem? Explain your choice. Construct a 97% confidence interval for the population proportion of adult Americans who feel that crime is the main problem.      i.   State the confidence interval,   ii.  Sketch the graph,  iii. Calculate the error bound 4.  Suppose we want to lower the sampling error. What is one way to accomplish that?

The dataset "nurses" is a random sample of 1,000 cases from “Health Care Provider Credential Data” from Washington State Open Data Portal. In the sample, there are 418 CNA's and 278 of the CNA's have expired credentials. Use the statistics from the nurses dataset to answer the following question: "With 90% confidence, what percent of all CNA's on Washington State's healthcare provider list are expired?"