Question

# You wish to test the following claim a significance level of α=0.10α=0.10. Ho:p=0.46Ho:p=0.46 Ha:p<0.46Ha:p<0.46 You obtain...

You wish to test the following claim a significance level of α=0.10α=0.10.

Ho:p=0.46Ho:p=0.46
Ha:p<0.46Ha:p<0.46

You obtain a sample of size n=326n=326 in which there are 121 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 0.46.
• There is not sufficient evidence to warrant rejection of the claim that the population proportion is less than 0.46.
• The sample data support the claim that the population proportion is less than 0.46.
• There is not sufficient sample evidence to support the claim that the population proportion is less than 0.46.

Solution :

Given that ,

n = 326

x = 121

The null and alternative hypothesis is

H0 : p = 0.46

Ha : p < 0.46

= x / n = 121 / 326 = 0.3712

P0 = 0.46

1 - P0 = 0.54

Test statistic = z

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

= 0.3712 - 0.46 / [0.46 ( 1- 0.46 ) / 326 ]

= -3.218

The test statisyic = -3.218

P-value = 0.0006

= 0.10

0.0006 < 0.10

P-value <

P - value is less than α

Reject the null hypothesis .

Conclusion : - There is sufficient evidence to warrant rejection of the claim that the population proportion is less than 0.46.

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