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the mean number of sick days an employee takes per year is believed to be about 10. Members of a personnel department do not believe this figure. They randomly survey B employees. The number of sick days that the mean number is about 107 Conduct a hypothesis test at the 5% level. they took for the past year are as follows: 12; 6; 14 5 11; 6;10. Lt X the number of sick days they took for the past year. Should the personnel teram belteve Note: If you are using a Students t-distribution for the problem, you may assume that the underlying population is normally distributed. n though.) (In general, you must first prove that assumption, ○Part (a) Part State the atermative hypothesis
Hrmwk Chapter 9 - Edit View Favorites Tools Help Part(c) In words, state what your random variable X represents ○ represents the average nmber of employees that call out sck for 10 days n one year O X represents the number of sick days an employee takes in one year O X represents the average number of employees that call out sick on a given day Xrepresents the average number of sick days employees take each year Part (d State the distribution to use for the test (Enter your answer in the form z or ta where df is the degrees of freedom) t-test E Part (e) What is the test statistic ? (f using the z distibution round your answers to two decimal places, and if using the f distribution round your answers to three decimal places) 0 937 Θ Part (n What is the pvalue? (Round your answer to four decimal places) 038 Explan what the pivalue means for this problem number of sck days for employees is at least as different from 10 as the mean of the sample is iferent r tots p-value that the ล.erage number of sck days for employees is at least as amerenthom 10 as me mean ofthe sample a diferentho O If He is false, then there is a chance equal to the p-value that the average
le Edit View Favonites Tools Help O If Hy is true, then there is a chance aqual to the p value the average number of sick days for employees O It H is faise, hen there is a chance equal to the pvalue the average number of sick is not at least as different from 10 as the mean of the sample is diferent from days for employees is not at least as different from 10 as the mean of the sample io different fronm a Part a) Sketch a picture of this situation Label and scale the horizontal axis and shade the region/s) corresponding to the p-value ap-value p-value 2p-value) 1/2p-value
Part (h) Part () Construct a 95% confidence mtervul for the true ean Sketch the gaph of thc suton Label the port esbrate the confidence intenval (Round your answers to throe d places) 95% CI. Addsional Matesials Section 91
E Part (h) the correct decision Creject or do not reject the null hypothesis), the reason for it, and write an appropriate conclusion o) Alpha (Enter an exact number as an integer, fraction, or decimal.) (n) Decision O reject the null hypothesis O do not reject the null hypothesis () Reason for decision: Since α < p-value, we do not reject the null hypothesis. O Since a > p-value, we do not reject the null hypothesis O Since a > p-value, we reject the null hypothesis since α < p-value, we reject the null hypothesis (iv) Conclusion O There is sufficient evidence to conclude that the average number of sick days used per year by an employee is not equal to 10 days 。There is not sufficient evidence to conclude that the average number of sick days used per year by an employee is not equal to 10 days Θ part (i) Construct a 95% confidence interval for the true mean. Sketch the graph of the s places ) ation Label the pont est nate and the lower and upper bounds of the eo
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use have the datau on the no.o t Year bY 8 emplo In this problem oblem oe eiek days taken on the pas Let us suppose thot the no. o sick dary s R2Xg is dnawn where both ape unkn oon Populaton, whene both parpometeps ene uwe have to te st_ cwhere lO tore he tos staksHc testn H o nstaisne cohere x= sample mean-n(-X,, sample s.d we peeet Ho ag. H, a+-level α.ee- me given samples the ndisho botion 3otheouise we aecept Mo In this ppoblem に8,15 3.412Con· dence limits Note 1-α = 0.95 #5-3. 4127(-ques, 2.84) 229 ) 8.75 3 31y2x 28 ч 1 229 e 5.3 226) 12 144

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