Consider the following hypothesis statement using alphaequals=0.10 and the follo

Question

Consider the following hypothesis statement using

alphaequals=0.10

and the following data from two independent samples. Complete parts a and b below.

Upper H 0 : p 1 minus p 2 greater than or equals 0H0: p1p20

x 1x1equals=57

x 2x2equals=48

Upper H 1 : p 1 minus p 2 less than 0H1: p1p2<0

n 1n1equals=150

n 2n2equals=120

Click here to view page 1 of the standard normal table.

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Click here to view page 2 of the standard normal table.

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a. Calculate the appropriate test statistic and interpret the result.

What is the test statistic?

nothing

(Round to two decimal places as needed.)

What are the critical values? round to three decimals

Does it reject or not reject?

b. What is the P value? round to three decimals

Does it reject or not reject?

Upper H 0 : p 1 minus p 2 greater than or equals 0H0: p1p20

x 1x1equals=57

x 2x2equals=48

Upper H 1 : p 1 minus p 2 less than 0H1: p1p2<0

n 1n1equals=150

n 2n2equals=120

Explanation / Answer

Given that,
sample one, x1 =57, n1 =150, p1= x1/n1=0.38
sample two, x2 =48, n2 =120, p2= x2/n2=0.4
null, Ho: p1 >= p2
alternate, H1: p1 < p2
level of significance, = 0.1
from standard normal table,left tailed z /2 =1.282
since our test is left-tailed
reject Ho, if zo < -1.282
we use test statistic (z) = (p1-p2)/(p^q^(1/n1+1/n2))
zo =(0.38-0.4)/sqrt((0.389*0.611(1/150+1/120))
zo =-0.335
| zo | =0.335
critical value
the value of |z | at los 0.1% is 1.282
we got |zo| =0.335 & | z | =1.282
make decision
hence value of |zo | < | z | and here we do not reject Ho
p-value: left tail - Ha : ( p < -0.335 ) = 0.36882
hence value of p0.1 < 0.36882,here we do not reject Ho
ANSWERS
---------------
a.
null, Ho: p1 >= p2
alternate, H1: p1 < p2
test statistic: -0.335 = -0.33
critical value: -1.282 = - 1.28
b.
decision: do not reject Ho
p-value: 0.36882 = 0.368

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