Population Standard Deviation

September 13, 2017 Communication

REVIEW EXERCISES CHAPTER 8 AND 9 PROFESSOR JONAS WIU-RES BY DEBRA JAMES CHAPTER 8 1. High temperature in the United States a meteorologist claims that the average of the highest temperatures in the united states in 98. A random sample of 50 cities is selected, and the highest temperatures are recorded. The data are shown. At a=0. 05 can the claim be rejected? a=7. 7 97, 101, 99, 99, 100, 94, 87, 99, 108, 93, 96, 88, 98, 97,88, 105, 97, 96, 98, 102, 99, 94, 96, 114, 99, 96, 98, 97, 91, 98, 80, 95, 98, 96, 80, 95, 88, 99, 102, 95, 101, 94, 92, 99, 101, 97, 94, 97, 102, 61.

The claim can be rejected; correct answer may be either above 98 or below it. 2. Salaries for Actuaries nationwide graduates entering the actuarial field earn $40,000. A college placement officer feels that this number is too low. She surveys 36 graduates entering the actuarial field and finds the average salary to be $41,000. The population standard deviation is $3000. Can her claim be supported at 0. 05? x? =14. 7, ? x? =13. 77, ox? =5. 34, n=29, ? =. 01 3. Monthly Home Rent. The average monthly rent for a one bedroom in San Francisco is $ 1229.

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A random sample of 15 one bedroom homes about 15 miles outside of San Francisco had a mean rent of $1350. The population standard deviation is $250. At a=0. 05 can we conclude that the monthly rent outside San Francisco differs from that in the city? 4. 5. Federal Prison Populations nationally 60. 2% of federal prisons are severing time for drug offenses. A warden feels that in his prisons the percentage is even higher. He surveys 400 inmates records and finds that 260 of the inmates are drug offenders at a=0. 5 is this correct? CHAPTER 9 1. Driving for pleasure – two groups of drivers is surveyed to see how many miles per week they drive for pleasure trips. The data are shown at a=0. 01 can it be conducted that single drivers do more driving for pleasure trips on average than married drivers? Assume =16. 7 and =16. 1 Level of significance a = 0. 05, we reject the null hypothesis. This means there is a significant difference between … There is not sufficient evidence to conclude. 2.

Communication times – according to the bureau of labor statistics American time use survey married persons spend an average of 8 minutes per day on phones calls, mail and email, while single persons spend an average of 14 minutes per day on these same tasks. Based on the following information is there sufficient evidence to conclude that single persons spend, on average a greater time each day communicating? Use the 0. 05 level of significance. There is not enough information to … actual average salary. In each of the following … At the 0. 05 level, does this show sufficient evidence to conclude . Teachers’ Salaries – a sample of 15 teachers from Rhode Island has an average salary of $35,270, with a standard deviation of $3256. A sample of 30 teachers from New York has an average salary of $29,512, with a standard deviation of $ 1431. Is there a significant difference in teachers’ salaries between the two states? Use a = 0. 02. Find the 98% confidence interval for the difference of the two means. H0: ? 1 – ? 2 = 3000 H1: ? 1 – ? 2 ? 3000 where, H0 is the null hypothesis, d = 3000 For hypothesis testing on two means with known variances: ? = [(X1 – X2) – d] / {v[ (? 1? n1) + (? 2? / n2) ] } where, X1 and X2 are the two sample means ?1 and ? 2 are the two sample standard deviations n1 and n2 are the two sample sizes In this case, X1 = 35,270 X2 = 29,512 ?1 = 3,256 ?2 = 1,432 n1 = 36 n2 = 49 d = 3,000 Plug these values into the above equation to obtain: ? = 4. 756 For a significance level of 2. 5% (i. e. 0. 025), Z = 2. 24 Since ? > Z at the 2. 5% significance level, the null hypothesis is rejected meaning that the data does not support the idea that a Rhode Island Teacher’s mean salary is $3,000 more than a New York Teacher’s mean salary. . High and Low Temperatures – March is a month of variable weather in the northeast. The chart below records the actual high and low temperatures for a selection of days in March from the weather reports for Pittsburgh Pennsylvania. At the 0. 01 level of significance is there sufficient evidence to conclude that there is more than a 10% difference between average highs and lows? Professor Jonas, I have not had a good time with this assignment, it is very hard working with one hand.

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