In making plans for an executive traveler’s club, an airline would like to estimate the proportion of its current customers who would qualify for membership. a random sample of 500 customers yielded 40 who would qualify.

(a) test the hypothesis h0 : p = 0.05 vs ha : p < 0.05 by constructing reject region at α = 0.1 state what action the airline should take.
(b) compute the p-value using r.

a)

So the rejection zone would be given by In our case since the estimated proportion is 0.08 we are not on the rejection zone so we FAIL to reject the null hypothesis.

b) prop.test(40, 500, p = 0.05,alternative = c("less"),conf.level = 0.95, correct = FALSE)

With the following output

1-sample proportions test without

continuity correction  

data:  40 out of 500, null probability 0.05

X-squared = 9.4737, df = 1, p-value = 0.999

alternative hypothesis: true p is less than 0.05

95 percent confidence interval:

0.000000 0.102291

sample estimates:

 p

0.08

Step-by-step explanation:

Data given and notation

n=500 represent the random sample taken

X=40 represent the customers who would qualify for membership

estimated proportion of adults that said that it is morally wrong to not report all income on tax returns

is the value that we want to test

represent the significance level

z would represent the statistic (variable of interest)

Alternative hypothesis:  

When we conduct a proportion test we need to use the z statisitc, and the is given by:  

(1)  

The One-Sample Proportion Test is used to assess whether a population proportion is significantly different from a hypothesized value .

Part a

The population proportion have the following distribution

And we know that the z score is given by:

And we are interested to find the value of

And if we solve for

So the rejection zone would be given by In our case since the estimated proportion is 0.08 we are not on the rejection zone so we FAIL to reject the null hypothesis.

Part b

prop.test(40, 500, p = 0.05,alternative = c("less"),conf.level = 0.95, correct = FALSE)

With the following output

1-sample proportions test without

continuity correction  

data:  40 out of 500, null probability 0.05

X-squared = 9.4737, df = 1, p-value = 0.999

alternative hypothesis: true p is less than 0.05

95 percent confidence interval:

0.000000 0.102291

sample estimates:

 p

0.08

i do not know the answer

step-by-step explanation: