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Page 1 of 3 STATISTICS - Show all your work for all questions, not just the final answer. Clearly label 1. A survey asked adult Americans (18 years or older) whether they used social media regularly. The result shows in table below: 18 - 34 35 - 44 45 - 54 55 + Use social media 117 89 83 49 Do not use social media 33 36 57 66 a). If an adult American is randomly selected, what is the probability he or she does not use social media? b). If an adult American is randomly selected, what is the probability he or she is 18 to 34 years old? c). If an adult American is randomly selected, what is the probability he or she is 45 to 54 years old and use social media? d). If an adult American is randomly selected, what is the probability he or she is 45 to 54 years old or use social media? 2. Assume that 70% of adults always wash their hands after using a public restroom. a. Find the probability that among 8 randomly selected adults, exactly 5 always wash their hands after using a public restroom b. Find the probability that among 8 randomly selected adults, at least 7 always wash their hands after using a public restroom. c. For groups of 8 randomly selected adults, find the mean and standard deviation of the numbers in the groups who always wash their hands after using a public restroom. d. If 8 adults are randomly selected, and it is found that exactly 1 of them washes hands after using a public restroom, is that a significantly low number? 3. A sociologist intends to estimate the percentage of adults who believe in astrology. How many adults does the sociologist need to survey if a confidence level of 90% and a margin error of 5% are desired? Page 2 of 3 a) if nothing is known about the percentage to be estimated. b) if a recent survey shows 16% of respondents say they believe in astrology. 4. This question explores the effect of the sample size on the sampling distribution of the mean. a) Open Excel. Select Data Analysis, then select “Random Number Generation” from the available options. Use the following values when prompted to enter them: There will be 80 rows and 7 columns filled with numbers in a new Sheet on Excel. Consider each row as a random sample drawn uniformly from the numbers 1 to 10. In this case, you have 80 samples of size 7. In the first empty cell of the following empty column, enter a formula for the mean of the sample in the first row, then drag this formula down to the last row. In this case, you should enter the formula =AVERAGE(A1:G1) into cell H1. Dragging the formula down from cell H1 to H80 to find the remaining sample means. b) Create a histogram for the sampling distribution of the mean using the upper class limits 1, 2, 3, . . . , 10. Edit the chart so that it reads “Created by (Your Name)” as the title. Rename the “Bin” column so that it includes lower and upper class limits (make the entries 0 to 1, 1.001 to 2, 2.001 to 3, 3.001 to 4, and so on). Set the gap width to 0%. Submit a screenshot of the histogram with its frequency distribution table. c) Repeat a) and b) with Number of Variables as 20 instead of 7. d) How does the sampling distribution of the mean change as the sample size increases? 5. A randomly selected group of 18 adults participated in a sleep study. The mean number of hours slept was x = 6.8 hours. The number of hours slept by adults seems to be normally distributed with mean 7 hours and standard deviation 2 hours. Page 3 of 3 a) Describe the sampling distribution of the sample mean x. b) What is the probability of drawing a sample of 18 adults with a mean of 6.8 hours of sleep or less? Give your answer as a percentage rounded to 3 decimal places. 6. In a random sample of 1500 adults, 460 of the respondents have sleepwalked. a) Let p represent the proportion of all adults who have sleepwalked. Find a point estimate for p rounded to 3 decimals places. b) Find 90% and 99% confidence intervals for p, again rounded to 3 decimal places. c) Using your 99% confidence interval from part b), make a conclusion about the results of drawing the sample. d) Describe what happens to the width of the confidence interval as the level of confidence increases.