Question

You wish to test the following claim (HaHa) at a significance level of α=0.05α=0.05.

      Ho:p=0.46Ho:p=0.46
      Ha:p≠0.46Ha:p≠0.46

You obtain a sample of size n=750n=750 in which there are 335 successful observations. Use the normal distribution as an approximation for the binomial distribution.

What is the test statistic for this sample? (Report answer accurate to three decimal places.)
test statistic =

What is the p-value for this sample? (Report answer accurate to four decimal places.)
p-value =

The p-value is...

• less than (or equal to) αα
• greater than αα

This test statistic leads to a decision to...

• reject the null
• accept the null
• fail to reject the null

As such, the final conclusion is that...

• There is sufficient evidence to warrant rejection of the claim that the population proportion is not equal to 0.46.
• There is not sufficient evidence to warrant rejection of the claim that the population proportion is not equal to 0.46.
• The sample data support the claim that the population proportion is not equal to 0.46.
• There is not sufficient sample evidence to support the claim that the population proportion is not equal to 0.46.

Answer 1

Solution :

Given that,

= 0.46

1 - = 0.54

n = 750

x = 335

Level of significance = = 0.05

Point estimate = sample proportion = = x / n = 335 / 750 = 0.447

This a two tailed test.

Test statistics

z = ( - ) / *(1-) / n

= ( 0.447 - 0.46) / (0.46*0.54) /750

= -0.714

P-value

= 2*(P(Z <z ))

= 2* P(Z < -0.714)

= 2*0.2376

= 0.4752

The p-value is p = 0.4752, and since p = 0.4752 > 0.05, it is concluded that the null hypothesis is fails to rejected.

Conclusion:

There is not sufficient evidence to warrant rejection of the claim that the population proportion is not equal to 0.46.