Repeated student samples. Of all freshman at a large college, 16% made the dean’s list in the currentyear. As part of a class project, students randomly sample 40 students and check if those students madethe list. They repeat this 1,000 times and build a distribution of sample proportions.(a) What is this distribution called?(b) Would you expect the shape of this distribution to be symmetric, right skewed, or left skewed? Explainyour reasoning.(c) Calculate the variability of this distribution.(d) What is the formal name of the value you computed in (c)?(e) Suppose the students decide to sample again, this time collecting 90 students per sample, and they againcollect 1,000 samples. They build a new distribution of sample proportions. How will the variabilityof this new distribution compare to the variability of the distribution when each sample contained 40observations?

A statistics instructor wants to measure the effectiveness of his teaching skills in a class of 102 students (N = 102). He selects students by waiting at the door to the classroom prior to his lecture and pulling aside every third student to give him or her a questionnaire.       Is this sample design an example of random sampling? Explain.       Assuming that all students attend his class that day, how many students will the instructor select to complete his questionnaire?

A school newspaper reporter decides to randomly survey 15 students to see if they will attend Tet (Vietnamese New Year) festivities this year. Based on past years, she knows that 13% of students attend Tet festivities. We are interested in the number of students who will attend the festivities. O Part (a) O Part (b) O Part (c) Give the distribution of X. -O(0:0) O Part (d) How many of the 15 students do we expect to attend the festivities? (Round your answer to the nearest whole number.) student(s) O Part (e) Find the probability that at most 3 students will attend. (Round your answer to four decimal places.) O Part (f) Find the probability that more than 2 students will attend. (Round your answer to four decimal places.)

The Census Bureau gives this distribution for the number of people in American households in 2016. Family size 1 2 4 6. 7 Proportion 0.28 0.35 0.15 0.13 0.06 0.02 0.01 Note: In this table, 7 actually represents households of size 7 or greater. But for purposes of this exercise, assume that it means only households of size exactly 7. Suppose you take a random sample of 4000 American households. About how many of these households will be of size 2? Sizes 3 to 7? The number of households of size 2 is about The number of households of size 3 to 7 is about

Which is a negatively skewed distribution?

Let's examine the mean of the numbers 1, 2, 3, 4, 5, 6, 7, and 8 by drawing samples from these values, calculating the mean of each sample, and then considering the sampling distribution of the mean. To do this, suppose you perform an experiment in which you roll an eight-sided die two times (or equivalently, roll two eight-sided dice one time) and calculate the mean of your sample. Remember that your population is the numbers 1, 2, 3, 4, 5, 6, 7, and 8. The true mean (µ) of the numbers 1, 2, 3, 4, 5, 6, 7, and 8 is , and the true standard deviation (o) is The number of possible different samples (each of size n = 2) is the number of possibilities on the first roll (8) times the number of possibilities on the second roll (also 8), or 8(8) = 64. If you collected all of these possible samples, the mean of your sampling distribution of means (µM) would equal and the standard deviation of your sampling distribution of means (that is, the standard error or ɑm) would be The following chart…

The students in an Introductory Statistics class are asked to complete a survey about study habits. (a) does the study appear to use random sampling? yes or no (b) does the study appear to use random assignment? yes or no

The average final exam score for the statistics course is 82%. A professor wants to see if the average final exam score for students who are given colored pens on the first day of class is different. The final exam scores for the 14 randomly selected students who were given the colored pens are shown below. Assume that the distribution of the population is normal. 90, 78, 82, 59, 67, 71, 64, 78, 67, 57, 79, 86, 66, 56 What can be concluded at the the αα = 0.05 level of significance level of significance?  For this study, we should use    (t-test for a population mean,  z-test for a population proportion) The null and alternative hypotheses would be:       H0: (symbol) (symbol) ____              H1: (symbol) (symbol) ____               The test statistic (?,t,z) = ____  (please show your answer to 3 decimal places.) The p-value =  (Please show your answer to 4 decimal places.) The p-value is (symbol)  αα Based on this, we should  (accept, reject, fail to reject) the null hypothesis.…

The average final exam score for the statistics course is 74%. A professor wants to see if the average final exam score for students who are given colored pens on the first day of class is different. The final exam scores for the 14 randomly selected students who were given the colored pens are shown below. Assume that the distribution of the population is normal. 71, 72, 53, 61, 75, 55, 75, 74, 58, 50, 71, 84, 76, 53 What can be concluded at the the αα = 0.10 level of significance level of significance? The null and alternative hypotheses would be:       H0: μ = ______________ H1: μ ≠ ______________ The test statistic t= ________________(please show your answer to 3 decimal places.) The p-value = _______________________    (Please show your answer to 4 decimal places.)