A. Identify null and alternative hypothesis. B. Determine critical values. C. Fi

Question

A. Identify null and alternative hypothesis.

B. Determine critical values.

C. Find standardized test statistic z.

D. Determine to fail to reject or reject null hypothesis.

A sociologist claims that children ages 12-14 spent less time sleeping in 1981 than children ages 12-14 do today. A study was conducted in 1981 to find the time that children ages 12-14 spent sleeping on weekdays, with the accompanying results. Assume the population standard deviation is 0.5 hour. Recently a similar study was conducted, with the accompanying results. Assume the population standard deviation is 0.4 hour. At = 0.01, is there evidence to support the Click the icon to view the sleeping times from the two different studies.

Explanation / Answer

(A)

Data:    

n1 = 20   

n2 = 20   

x1-bar = 7.75   

x2-bar = 8.985   

1 = 0.5   

2 = 0.4   

Hypotheses:    

Ho: 1 2    

Ha: 1 < 2    

(B)

Decision Rule:    

= 0.01   

Critical z- score = -2.326347874   

Reject Ho if z < -2.326347874   

(C)

Test Statistic:    

SE = {(s1^2 /n1) + (s2^2 /n2)} = ((0.5)^2/20) + ((0.4)^2/20)) = 0.143178211

z = (x1-bar - x2-bar)/SE = (7.75 - 8.985)/0.143178210632764 = -8.625614153

p- value = 3.18748E-18   

(D)

Decision (in terms of the hypotheses):    

Since -8.625614153 < -2.326347874 we reject Ho and accept Ha

Conclusion (in terms of the problem):    

There is sufficient evidence to support the claim.   

    

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