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Sagot :
Answer:
a) The test statistic is [tex]z = -2.51[/tex]
b) The pvalue is 0.0060.
Step-by-step explanation:
Question a:
Ha: pB < pNY
This means that the alternate hypothesis is rewritten as:
[tex]H_a: p_{B} - p_{NY} < 0[/tex]
While the null hypothesis is:
[tex]H_0: p_{B} - p_{NY} = 0[/tex]
The test statistic is:
[tex]z = \frac{X - \mu}{s}[/tex]
In which X is the sample mean, [tex]\mu[/tex] is the value tested at the null hypothesis and s is the standard error
pB = 0.581, pNY = 0.832
This means that [tex]X = 0.581 - 0.832 = -0.251[/tex]
0 is tested at the null hypothesis:
This means that [tex]\mu = 0[/tex]
Standard error = 0.1
This means that [tex]s = 0.1[/tex]
Test statistic:
[tex]z = \frac{X - \mu}{s}[/tex]
[tex]z = \frac{-0.251 - 0}{0.1}[/tex]
[tex]z = -2.51[/tex]
The test statistic is [tex]z = -2.51[/tex]
Question b:
The pvalue is the probability of finding a proportion less than -0.251, that is, a difference of at least 0.251, which is the pvalue of Z = -2.51.
Looking at the z-table, Z = -2.51 has a pvalue of 0.0060
The pvalue is 0.0060.
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