A bank manager must decide whether or not to hire additional tellers. His decisi

Question

A bank manager must decide whether or not to hire additional tellers. His decision will depend how long it takes to complete customer transactions. The null hypothesis is that the mean transaction completion time, mu, is at most 40 seconds. The standard deviation is assumed to be 10 seconds. If the null is rejected, new tellers will be hired. A sample be 100 transactions was obtained with a mean of 42.5 seconds. The significance level is .05 a) State the Null and Alternate Hypothesis. b) Which test statistic does the data call for? c) State Decision Rule and Critical Value d) Compute the test statistic. e) What is your decision concerning Null? f) What (how much) is the probability of a Type I (alpha) error? g) What affect would a type I (alpha) error have on the bank and/or customers? h) What affect would a type l (alpha) error have on the bank and/or customers? William used a sample of 68 large U.S. cities to estimate the relationship between Crime (annual property crimes per 100,000 persons) and Income (median annual income per capita, in dollars). His estimated regression equation was Crime = 428 0.050 Income. a) Find the critical value(s) to see if the slope is negative, using alpha = 0.5 b) Find the critical value(s) to see if the slope is zero, using alpha = .05 c) If the Income increases, would you expect the Crime to increase or decrease? Explain. d) If Income increased by 1,000, how much would this model predict the change in Crime (make sure you indicate the direction (negative or positive) and the amount)? A news network stated that a study had found a positive correlation between the number of children a worker has and his or her earnings last year. a) If you have many children, would you expect to have higher earnings? b) Even if the correlation is high, would that show causality?

Explanation / Answer

Q.2 Null Hypothesis : H0 : The average hospitalization for triple Hernia operation is not more than 30 hours. <= 30 Hours

ALternative Hypothesis : Ha : The average hospitalization for triple Hernia operation is more than 30 hours. > 30 Hours

(b) we will use student' t test distribution for the sample. Here we choose t - distribution because sample size is less than 30.

(c) Decision rule is here if the value of sample mean is under the confidence interval of population null hypothesis mean of 30 hours than we will not reject the null hypothesis .

Critical value fro alpha = 0.025 and dF = 16-1 = 15 is tcritical = 2.131

(d) Test Statistic

t = (xbar-   H)/ (s/n) = ( 40 - 30) / (20/ 16) = 10/ ( 20/4) = 2

so here p - value from table is = 0.0639

(e) We cannot reject the null hypothesis

(f) tnew = (xbar-   H)/ (s/n) = ( 40 - 30) / (20/ 225) = 10/ ( 20/15) = 7.5

(g) We will reject the null hypothesis then as tnew > tcritical

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