NYC has the busiest subway system in the US with a weekly verage number of passe
ID: 3134121 • Letter: N
Question
NYC has the busiest subway system in the US with a weekly verage number of passengers of 4.6 million nd a standard deviation of 1.1 million. test whether a sample of 50 days producing a mean of 4.8 million is significantly greater using the significance level of 0.025.
a. What is the direction of the null hypothesis?
b. What is the direction of the critical region?
c. What is the calculated value of the test statistic? (rounded to the hundredth place)
d. What is the P-value? (rounded to the ten thousandths place (4 digits))
e. The decision is to fail to reject the null hypothesis. True or False?
f. The decision implies that the evidence shows the mean number of passengers equals 4.6 million. True or False?
Explanation / Answer
a)
Formulating the null and alternative hypotheses,
Ho: u <= 4.6
Ha: u > 4.6
As we can see, this is a right tailed test. [ANSWER, RIGHT TAILED]
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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 = 4.8
uo = hypothesized mean = 4.6
n = sample size = 50
s = standard deviation = 1.1
Thus, z = (X - uo) * sqrt(n) / s = 1.285648693 [ANSWER, TEST STATISTIC]
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d)
Also, the p value is
p = 0.099282847 [ANSWER, P VALUE]
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e)
As P > 0.025, we FAIL TO REJECT THE NULL HYPOTHESIS. [ANSWER: TRUE]
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f)
FALSE. There simply is no evidence that the true mean is not greater than 4.6 million, but we cannot say if it is truly 4.6 million. [Note: This is the interpretation in many classes, it can be TRUE in some classes. Please use the convention of interpretation used in your class. It depends on how strict we are in formalities, and this is a strict formality. Thanks!]
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