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 0.32. A random sample of 715 men over the age of 50 found that 196 have their prostate regularly examined. Do the sample data provide convincing evidence to support the claim? Test the relevant hypotheses using a 10% 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: H1: Based on the hypotheses, find the following: Test Statistic = Critical-value = (Hint: Look up critical value online. This is the z-score that represents the boundary for the level of significance. Use invNorm to find the z-score that corresponds to your significance level.) 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: . Click and drag the arrows to adjust the values. Normal curveInterval pointer-1.5 The correct decision is to . The correct summary would be: that the proportion of men over the age of 50 who regularly have their prostate examined is significantly less than 0.32.

Answer 1

Let the population proportion of men over the age 50 who regularly have their prostate examined be denoted by p.

The null and the alternative hypotheses are given by

The given data is summarized as follows:

Sample size(n)=715

Sample proportion:

The test statistic is given by

The test statistic under the null hypothesis follows standard normal distribution. The critical value at 5% level of significance is obatined from the Biometrika table as

As the observed value is greater than the test statistic, we fail to reject the null hypothesis at 5% level of significance and hence conclude that the claim is not justified i.e. the population proportion of men over the age 50 who regularly have their prostate examined is not significantly less than 0.32 at 5% level of significance.

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