In: Statistics and Probability
Recall the framework for a hypothesis test:
1. Identify the parameter or parameters about which you need to make a decision.
2. State a null hypothesis H0 and an alternative hypothesis Ha about your parameter.
3. Choose a significance level α. Typical values are 0.05, 0.1, or 0.01.
4. Calculate and standardize your test statistic. It will be the statistic that estimates your parameter.
5. Calculate a p-value. Your technology will handle this.
6. Make a decision: Either reject H0 or fail to reject H0.
7. Interpret your decision in context.
1. The CEO of a large electric utility claims that 80 percent of his customers are very satisfied with the service they receive. To test this claim, the local newspaper surveys 100 customers, using simple random sampling. Among the sampled customers, 73 of them say they are very satisfied. Based on these findings, can we reject the CEO's hypothesis that 80% of the customers are very satisfied
Given that,
possibile chances (x)=73
sample size(n)=100
success rate ( p )= x/n = 0.73
success probability,( po )=0.8
failure probability,( qo) = 0.2
null, Ho:p=0.8
alternate, H1: p!=0.8
level of significance, α = 0.05
from standard normal table, two tailed z α/2 =1.96
since our test is two-tailed
reject Ho, if zo < -1.96 OR if zo > 1.96
we use test statistic z proportion = p-po/sqrt(poqo/n)
zo=0.73-0.8/(sqrt(0.16)/100)
zo =-1.75
| zo | =1.75
critical value
the value of |z α| at los 0.05% is 1.96
we got |zo| =1.75 & | z α | =1.96
make decision
hence value of |zo | < | z α | and here we do not reject
Ho
p-value: two tailed ( double the one tail ) - Ha : ( p != -1.75 ) =
0.08012
hence value of p0.05 < 0.0801,here we do not reject Ho
ANSWERS
---------------
1.
the parameter or parameters about which you need to make a decision
is Z test for proportion
2.
null, Ho:p=0.8
alternate, H1: p!=0.8
3.
i.
level of significance =0.05
ii.
level of significance =0.01
critical value
the value of |z α| at los 0.01% is 2.576
we got |zo| =1.75 & | z α | =2.576
make decision
hence value of |zo | < | z α | and here we do not reject
Ho
p-value: two tailed ( double the one tail ) - Ha : ( p != -1.75 ) =
0.08012
hence value of p0.01 < 0.0801,here we do not reject Ho
ANSWERS
---------------
null, Ho:p=0.8
alternate, H1: p!=0.8
test statistic: -1.75
critical value: -2.576 , 2.576
decision: do not reject Ho
p-value: 0.08012
iii.
level of significance =0.10
critical value
the value of |z α| at los 0.1% is 1.645
we got |zo| =1.75 & | z α | =1.645
make decision
hence value of | zo | > | z α| and here we reject Ho
p-value: two tailed ( double the one tail ) - Ha : ( p != -1.75 ) =
0.08012
hence value of p0.1 > 0.0801,here we reject Ho
ANSWERS
---------------
null, Ho:p=0.8
alternate, H1: p!=0.8
test statistic: -1.75
critical value: -1.645 , 1.645
decision: reject Ho
p-value: 0.08012
we have enough evidence to support the claim that 80 percent of his
customers are very satisfied with the service they receive.
4.
test statistic: -1.75
critical value: -1.96 , 1.96
5.
p-value: 0.08012
6.
decision: do not reject Ho
7.
we do not have enough evidence to support the claim that 80 percent
of his customers are very satisfied with the service they
receive.