Question

MAT2058 Statistics sU03 Test: Week 5 Final Exam This 15 pts 18 of 20 (17 of an adverse H, p#080 H, pc0 20 H, p>0 20 peo 8 OF. HP-020 n, p#020 The P-yae isRound to four decimal places as needed) dentily the conckusion about the null hypothesis and the final conclusion thait addresses the original dlaim program

Answer 1

To test
Ho : p 0.20
against
1:p 0.20

Here

sample proportion

p = 0.15

and sample size

n6000

The test statistic can be written as

which under H₀ follows a standard normal distribution.

p-0.20 0.20+(1-0.20) 7t

We reject H₀ at 1% level of significance if P-value < 0.01

Now,

The value of the test statistic

~obs= 9.68246

and P-value

P(Z < zobs) = P(Z <-9.68246) = 0

Since p-value < 0.01, so we reject H₀ at 1% level of significance and we can conclude that there is sufficient evidence to support the claim that less than 20% of the TV sets in use were found to the program.