Question

You are conducting a study to see if the proportion of men over the age of 50 who regularly have their prostate examined is significantly less than 0.3. A random sample of 726 men over the age of 50 found that 205 have their prostate regularly examined. Do the sample data provide convincing evidence to support the claim? Test the relevant hypotheses using a 1% level of significance. Give answer to at least 4 decimal places.

What are the correct hypotheses? (Select the correct symbols and use decimal values not percentages.)

H₀: Select an answer x̄ σ² p p̂ s σ μ s²  ? ≠ ≥ = < ≤ >  

H₁: Select an answer p s² σ μ x̄ p̂ σ² s  ? = < ≠ ≥ ≤ >  

Based on the hypotheses, find the following:

Test Statistic =

Critical-value=

Shade the sampling distribution curve with the correct critical value(s) and shade the critical regions. The arrows can only be dragged to z-scores that are accurate to 1 place after the decimal point (these values correspond to the tick marks on the horizontal axis). Select from the drop down menu to shade to the left, to the right, between or left and right of the z-score(s).

Shade: Left of a valueRight of a valueBetween two values2 regions. Click and drag the arrows to adjust the values.

-1.5

The correct decision is to Select an answer Accept the null hypothesis Fail to reject the null hypothesis Accept the alternative hypotheis Reject the null hypothesis  .

The correct summary would be: Select an answer There is enough evidence to support the claim There is not enough evidence to support the claim There is not enough evidence to reject the claim There is enough evidence to reject the claim  that the proportion of men over the age of 50 who regularly have their prostate examined is significantly less than 0.3.

Answer 1

Given : n=726 , X=205 , The estimate of the sample proportion is ,

The null and alternative hypothesis is ,

The test is one-tailed test.

The test statistic is ,

The critical value is ,

; From Z-table

Decision : Here , the value of the test statistic does not lies in the rejection region.

Therefore , fail to reject the null hypothesis.

Conclusion : There is enough evidence to reject the claim  that the proportion of men over the age of 50 who regularly have their prostate examined is significantly less than 0.3.