Mr. Smith Claims that students at Bamfield College of Aeronautic have a higher g

Question

Mr. Smith Claims that students at Bamfield College of Aeronautic have a higher grade point average that those who attend who attend the Aviation College in Mar del Plata. The information below was collected at the two higher education institutions. Is there sufficient proof to reject Mr. Smith claim? Use alpha of 0.1 to test the claim. (Please show all pertinent steps of conducting this hypothesis testing) 1. Mar Del Plata Sample size 59 population SD-0.66 Sample mean 3.05 Bamfield Sample size 46 population SD= 0.79 Sample mean = 3.26

Explanation / Answer

Given that,
mean(x)=3.05
standard deviation , 1 =0.66
number(n1)=59
y(mean)=3.26
standard deviation, 2 =0.79
number(n2)=46
null, Ho: u1 > u2
alternate, H1: 1 < u2
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) = (x-y)/sqrt(s.d1^2/n1)+(s.d2^2/n2)
zo=3.05-3.26/sqrt((0.4356/59)+(0.6241/46))
zo =-1.45
| zo | =1.45
critical value
the value of |z | at los 0.1% is 1.282
we got |zo | =1.451 & | z | =1.282
make decision
hence value of | zo | > | z | and here we reject Ho
p-value: left tail - Ha : ( p < -1.45 ) = 0.07341
hence value of p0.1 > 0.07341,here we reject Ho
ANSWERS
---------------
null, Ho: u1 = u2
alternate, H1: 1 < u2
test statistic: -1.45
critical value: -1.282
decision: reject Ho
p-value: 0.07341

we have evidence to support the claim

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