Conduct a hypothesis test for each problem, using the traditional method. Show t
ID: 3155928 • Letter: C
Question
Conduct a hypothesis test for each problem, using the traditional method. Show the 5 steps and all work for each hypothesis test.
A reading group claims that Americans read more as they grow older. A random sample of 45 Americans age 60 or older read for a mean length of 62.8 minutes per day, with a population standard deviation of 18.3 minutes per day. A random sample of 88 Americans between the ages of 50 and 59 read for a mean length of 54.2 minutes per day, with a population standard deviation of 23.1 minutes per day. At the 0.01 level of significance, test the claim that the mean time spent reading per day by Americans age 60 and older is longer than the mean time spent reading per day by Americans between the ages of 50 and 59.
Explanation / Answer
Formulating the null and alternative hypotheses,
Ho: u1 - u2 <= 0
Ha: u1 - u2 > 0
At level of significance = 0.05
As we can see, this is a right tailed test.
Calculating the means of each group,
X1 = 62.8
X2 = 54.2
Calculating the standard deviations of each group,
s1 = 18.3
s2 = 23.1
Thus, the standard error of their difference is, by using sD = sqrt(s1^2/n1 + s2^2/n2):
n1 = sample size of group 1 = 45
n2 = sample size of group 2 = 88
Also, sD = 3.675017007
Thus, the z statistic will be
z = [X1 - X2 - uD]/sD = 2.340125225
where uD = hypothesized difference = 0
Now, the critical value for z is
zcrit = 2.33
Also, using p values, as this is right tailed,
Pvalue = 0.009638638
As z> 2.33, and P < 0.01, we reject Ho.
There is significant evidence at 0.01 level that the mean time spent reading per day by Americans age 60 and older is longer than the mean time spent reading per day by Americans between the ages of 50 and 59. [CONCLUSION]
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