Question

You wish to test the following claim a significance level of α=0.05α=0.05.

Ho:p=0.14Ho:p=0.14

Ha:p<0.14Ha:p<0.14

You obtain a sample of size n=268n=268 in which there are 19 successful observations.

- What is the test statistic for this sample?

test statistic = Round to 3 decimal places. - What is the p-value for this sample?

P-value = Use Technology Round to 4 decimal places. - 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 less than 0.14.
- There is not sufficient evidence to warrant rejection of the claim that the population proportion is less than 0.14.
- The sample data support the claim that the population proportion is less than 0.14.
- There is not sufficient sample evidence to support the claim that the population proportion is less than 0.14.

Answer #1

Solution :

This is the left tailed test .

The null and alternative hypothesis is

H0 : p = 0.14

Ha : p < 0.14

n = 268

x = 19

= x / n = 268 / 19 =0.07

P0 = 0.14

1 - P0 = 1 - 0.14 = 0.86

Test statistic = z

= - P0 / [P0 * (1 - P0 ) / n]

=0.07 -0.14 / [(0.14*0.84) / 268 ]

= -3.299

Test statistic = z = -3.299

P(z < -3.299 ) = 0.0073

P-value = 0.0073

= 0.05

P-value <

0.0073 < 0.05

Reject the null hypothesis .

There is sufficient evidence to warrant rejection of the claim that the population proportion is less than 0.14.

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