QUESTION 19 Suppose the time that it takes a certain large bank to approve a hom

Question

QUESTION 19 Suppose the time that it takes a certain large bank to approve a home loan is Normally distributed with rnean (in days) and standard deviation = 1·The bank advertises that it approve loans in 5 days, on average, but measurements on a random sample of 500 loan applicationsto hisbank gave a mean approval time of 5.3 days. Is thisa stron that the mean time to approval is actually longer than advertised? To answer this, test the hypotheses Ho: 5, Ha: > 5 at significance level 0.01. You conclude that g evidence a. Ho should be rejected. b. Ho should not be rejected. c. Ha should be rejected. d, there is a 5% chance that the null hypothesis is true.

Explanation / Answer

19.

Given that,
population mean(u)=5
standard deviation, =1
sample mean, x =5.3
number (n)=500
null, Ho: <=5
alternate, H1: >5
level of significance, = 0.01
from standard normal table,right tailed z /2 =2.326
since our test is right-tailed
reject Ho, if zo > 2.326
we use test statistic (z) = x-u/(s.d/sqrt(n))
zo = 5.3-5/(1/sqrt(500)
zo = 6.708
| zo | = 6.708
critical value
the value of |z | at los 1% is 2.326
we got |zo| =6.708 & | z | = 2.326
make decision
hence value of | zo | > | z | and here we reject Ho
p-value : right tail - ha : ( p > 6.708 ) = 0
hence value of p0.01 > 0, here we reject Ho
ANSWERS
---------------
null, Ho: <=5
alternate, H1: >5
test statistic: 6.708
critical value: 2.326
decision: reject Ho
p-value: 0
we have enough evidence to support the claim
option :a

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