SOLUTION: The Business Management Institute claims that 60% of their members like their jobs. A total of 900 members were surveyed as to whether they liked their job of which 450 members res

Question 1171769: The Business Management Institute claims that 60% of their members like their jobs. A total of 900 members were surveyed as to whether they liked their job of which 450 members responded that they liked their job. Given this information test the Institute’s claim.
a. Calculate the sample proportion and determine if you can use the normal distribution.
b. State the null and alternative hypothesis.
c. Compute the test statistic.
d. The theoretical statistic.
e. Test the claim.
Answer by Boreal(15235) (Show Source): You can put this solution on YOUR website!
point estimate is 450/900 =0.5. Can use normal distribution here because np and n(1-p) are both > 10.
Ho: proportion is 0.60
Ha: proportion is not 0.60
let alpha be 0.05 p{reject Ho|Ho true}
test is z for a 1 sample proportion
critical value is |z| > 1.96
z=(p hat-p)/sqrt(0.6*0.4/900)
=-0.10/.0.0163
=-6.12
strongly reject Ho, and it is not 60% of their members like their jobs.
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