Determine the value for the standardized test statistic z to

Determine the value for the standardized test statistic z to test the claim about the population proportion p>.03 given n=220 and sample proportion equal to .038. use =.05.

DO NOT USE MINITAB PLEASE.

TI calculators is ok or better yet actually solve please. thank you!

Solution

We have to calculate the test statistic value to test the claim that

H0 : p = 0.03 Vs H1 : p > 0.03

n = 220

p is population proportion = 0.03

sample proportion (p^) = 0.038

alpha = 0.05

The test statistic for testing single proportion is,

Z = (p^ - p) / sqrt [ p*q/n ]

q = 1 - p = 1 - 0.03 = 0.97

Z = (0.038 - 0.03) / sqrt [(0.03*0.97)/220 ]

Z = 0.008 / sqrt [0.0001323]

Z = 0.6956

The standardized test statistic is 0.6956

P-value we can calculate by using EXCEL.

syntax :

=NORMSDIST(z)

where z is test statistic value

P-value = 1 - 0.7580 = 0.2420 (the alternative is right sided)

P-value > 0.05

Accept H0 at 0.05 significance level.

Conclusion : Population proportion is greator than 0.03