H0 : 220 H1 : < 220 A sample of 64 observations is selected from a normal popula
ID: 3132334 • Letter: H
Question
H0 : 220 H1 : < 220 A sample of 64 observations is selected from a normal population. The sample mean is 215, and the population standard deviation is 15. Conduct the following test of hypothesis using the .025 significance level. a. Is this a one- or two-tailed test? Two-tailed test One-tailed test b. What is the decision rule? (Negative amount should be indicated by a minus sign. Round your answer to 2 decimal places.) (Click to select)Do not rejectReject H0 when z < c. What is the value of the test statistic? (Negative amount should be indicated by a minus sign. Round your answer to 3 decimal places.) Value of the test statistic d. What is your decision regarding H0? Reject Do not reject e. What is the p-value? (Round your answer to 4 decimal places.) p-value
Explanation / Answer
a)
Formulating the null and alternative hypotheses,
Ho: u >= 220
Ha: u < 220
As we can see, this is a left tailed test.
Hence, it is ONE TAILED. [ANSWER]
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b)
Thus, getting the critical z, as alpha = 0.025 ,
alpha = 0.025
zcrit = - 1.959963985
Hence, Reject Ho when z < -1.96. [ANSWER]
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c)
Getting the test statistic, as
X = sample mean = 215
uo = hypothesized mean = 220
n = sample size = 64
s = standard deviation = 15
Thus, z = (X - uo) * sqrt(n) / s = -2.666666667 [ANSWER]
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d)
As z < -1.96, we REJECT HO. [ANSWER]
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e)
As this is one tailed, the p value is
p = 0.003830381 [ANSWER]
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