You are conducting a study to see if the proportion of men over the age of...

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.

Solutions

Expert Solution

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.

Hopefully this will help you. In case of any query, do comment. If you are satisfied with the answer, give it a like. Thanks.

orchestra answered 1 year ago

Next > < Previous

Related Solutions

You are conducting a study to see if the proportion of men over 50 who regularly...

You are conducting a study to see if the proportion of men over 50 who regularly have their prostate examined is significantly more than 0.57. You use a significance level of α = 0.001 H 0 : p = 0.57 H1:p>0.57 You obtain a sample of size n=273 in which there are 177 successes. What is the test statistic for this sample? (Report answer accurate to three decimal places.) test statistic = What is the p-value for this sample? (Report...

You are conducting a study to see if the proportion of men over 50 who regularly...

You are conducting a study to see if the proportion of men over 50 who regularly have their prostate examined is significantly less than 64%. With H1 : p < 64% you obtain a test statistic of z = − 1.241 . Find the p-value accurate to 4 decimal places.

You are conducting a study to see if the proportion of women over 40 who regularly...

You are conducting a study to see if the proportion of women over 40 who regularly have mammograms is significantly different from 0.81. You use a significance level of α = 0.05 . H 0 : p = 0.81 H 1 : p ≠ 0.81 You obtain a sample of size n = 627 in which there are 494 successes. What is the test statistic for this sample? (Report answer accurate to three decimal places.) test statistic = What is...

You are conducting a study to see if the proportion of voters who prefer Candidate A...

You are conducting a study to see if the proportion of voters who prefer Candidate A is significantly more than 47%. With Ha : p > 47% you obtain a test statistic of z = 1.997. Find the p-value accurate to 4 decimal places. p-value = You are conducting a study to see if the accuracy rate for fingerprint identification is significantly less than 0.62. Thus you are performing a left-tailed test. Your sample data produce the test statistic z...

You are conducting a study to see if the proportion of voters who prefer Candidate A...

You are conducting a study to see if the proportion of voters who prefer Candidate A is significantly more than 0.82. You use a significance level of α=0.10α=0.10. H0:p=0.82H0:p=0.82 H1:p>0.82H1:p>0.82 You obtain a sample of size n=202n=202 in which there are 181 successes. What is the p-value for this sample? (Report answer accurate to four decimal places.) p-value =

You are conducting a study to see if the proportion of voters who prefer the Democratic...

You are conducting a study to see if the proportion of voters who prefer the Democratic candidate is significantly larger than 58% at a level of significance of α = 0.10. According to your sample, 43 out of 73 potential voters prefer the Democratic candidate. For this study, we should use The null and alternative hypotheses would be: Ho: (please enter a decimal) H1: (Please enter a decimal) The test statistic = (please show your answer to 3 decimal places.)...

You are conducting a study to see if the proportion of voters who prefer the Democratic...

You are conducting a study to see if the proportion of voters who prefer the Democratic candidate is significantly different from 60% at a level of significance of α = 0.01. According to your sample, 48 out of 70 potential voters prefer the Democratic candidate. For this study, we should use The null and alternative hypotheses would be: Ho: (please enter a decimal) H1: (Please enter a decimal) The test statistic = (please show your answer to 3 decimal places.)...

You are conducting a study to see if the proportion of voters who prefer the Democratic...

You are conducting a study to see if the proportion of voters who prefer the Democratic candidate is significantly different from 54% at a level of significance of αα = 0.01. According to your sample, 51 out of 100 potential voters prefer the Democratic candidate. For this study, we should use Select an answer t-test for a population mean z-test for a population proportion The null and alternative hypotheses would be: Ho: ? p μ ? > ≠ = < (please enter...

You are conducting a study to see if the proportion of voters who prefer the Democratic...

You are conducting a study to see if the proportion of voters who prefer the Democratic candidate is significantly smaller than 55% at a level of significance of αα = 0.01. According to your sample, 26 out of 56 potential voters prefer the Democratic candidate. For this study, we should use Select an answer z-test for a population proportion t-test for a population mean The null and alternative hypotheses would be: Ho: ? μ p ? ≠ < = > (please enter...

You are conducting a study to see if the proportion of voters who prefer the Democratic...

You are conducting a study to see if the proportion of voters who prefer the Democratic candidate is significantly smaller than 73% at a level of significance of αα = 0.05. According to your sample, 49 out of 72 potential voters prefer the Democratic candidate. For this study, we should use Select an answer t-test for a population mean z-test for a population proportion The null and alternative hypotheses would be: Ho: ? p μ ? < > = ≠ (please enter...

Subjects