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...

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.

1. What is the test statistic for this sample?

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

P-value =  Use Technology Round to 4 decimal places.
3. The p-value is...
• less than (or equal to) αα
• greater than αα

4. This test statistic leads to a decision to...
• reject the null
• accept the null
• fail to reject the null

5. 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.

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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