STA 6166 – Exam 1 – Fall 2013 PRINT Name ___________________________Conduct all tests at = 0.05 significance levelQ.1. The father of a teenage child records the number of telephone calls the child receives or makes for each of five days. The results are: 9,6,12,7,6 a.What is the mean number of calls in one day?b.What is the median number of calls in one day?c.What is the standard deviation of the number of calls?Q.2. A school system employs teachers at salaries between $18,000 and $40,000. The teachers' union and the school board are negotiating the form of next year's increase. Circle the correct response to each of the following.p.2.a. If every teacher is given a flat $1,000 raise, what is the effect on each of the following measures of salaries?Mean: (1) decreases by $1,000 (2) increases by $1,000 (3) remains the sameStandard Deviation: (1) decreases by $1,000 (2) increases by $1,000 (3) remains the samep.2.b. If every teacher is given a 5% raise, the amount of the raise will vary from $900 to $2,000, depending on the teacher's current salary. What is the effect on each of the following descriptive measures of the salaries?Mean: (1) decreases by 5% (2) increases by 5% (3) remains the sameStandard deviation; (1) decreases by 5% (2) increases by 5% (3) remains the sameQ.3. In a population of birds on a desert island, 40% are Red, 30% are Yellow, 20% are Black, and 10% are Green. Amongthe Red birds, 5% have a genetic trait, among the Yellows, 10% have the trait, among the Blacks, 20% have the trait, andamong the Yellows, 25% have the trait. Let T be the event that a bird has the trait. Complete the following table.Q.4. A soccer player on the UF soccer team has a probability of scoring on a penalty kick against a particular goalie of =0.80. Suppose in the course of a game, she has 3 penalty kicks against the goalie. p.4.a. What is the probability she scores on all 3 kicks (assuming independence)?p.4.b. What is the probability she fails to score on all 3 kicks?p.4.c. Suppose each day she attempts 64 penalty kicks, and observes ^p, the sample proportion of successful attempts. Thesampling distribution of ^p is approximately:Shape ___________ Mean ____________________ Standard Error ___________________________Q.5. A random sample of n = 36 cars driving on a residential street had a sample mean of 38 miles/hour, and a standarddeviation of 12 miles per hour. p.5.a. Obtain a 95% Confidence Interval for the true population mean speed of all drivers on the street.p.5.b. Test whether the population mean speed exceeds the posted speed limit of 35 mph. H0: ≤ 35 HA: > 35Test Statistic: _____________ Rejection Region (Based on Z-dist) ___________ Approximate P-value: ________Q.6. A researcher wishes to estimate the true mean mercury level among adult fish in a large lake within 0.2 with 95%confidence. Based on a pilot study, she believes ≈ 5.0. How many fish will she need to sample?Q.7. A study compared using procyandin B-2 obtained from apples with a placebo on terminal hair growth (hairs > 60m)in men. The B-2sample had 19 subjects, and the placebo sample had 19 subjects. The following summary data wereobtained, where the response was increase in terminal hair over 6 months (negative increases are decreases).p.7.a. Obtain a 95% Confidence Interval for B2 - P assuming population variances are equal.p.7.b. Use the large-sample Wilcoxon Rank-Sum test to test whether Median Hair growth differs for B-2 and placebo. H0: MB2 = MP HA : MB2 ≠ MP Note: T = 18.23Test Statistic: _________________ Rejection Region: ________________ P-value: _______________p.7.c. This was a pilot study. Suppose they want to conduct a full-scale study, and a goal to be able to detect a differenceof = 1.00 with power = 1- = 0.80 and = 0.05 (2-sided test). How many people should be assigned to each treatmentassuming 2 = 8 for each
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