Question

1.      Out of 500 people sampled, 140 received flu vaccinations this year. Based on this, construct a 95% confidence interval for the true population proportion of people who received flu vaccinations this year.
Give your answers as decimals, to three places
< p <

2.      You are conducting a study to see if the proportion of men over 50 who regularly have their prostate examined is significantly more than 0.68. You use a significance level of α=0.05α=0.05.
                                                       H0:p=0.68H0:p=0.68
                                                       H1:p>0.68H1:p>0.68

You obtain a sample of size n=432n=432 in which there are 314 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 answer accurate to four decimal places.)
p-value =

The p-value is... less than (or equal to) ααgreater than αα
This test statistic leads to a decision to... reject the nullaccept the nullfail to reject the null                              As such, the final conclusion is that...

There is sufficient evidence to warrant rejection of the claim that the proportion of men over 50 who regularly have their prostate examined is more than 0.68.

There is not sufficient evidence to warrant rejection of the claim that the proportion of men over 50 who regularly have their prostate examined is more than 0.68.

The sample data support the claim that the proportion of men over 50 who regularly have their prostate examined is more than 0.68.

There is not sufficient sample evidence to support the claim that the proportion of men over 50 who regularly have their prostate examined is more than 0.68.

The effectiveness of a blood-pressure drug is being investigated. An experimenter finds that, on average, the reduction in systolic blood pressure is 47.3 for a sample of size 1066 and standard deviation 6.8. Estimate how much the drug will lower a typical patient's systolic blood pressure (using a 95% confidence level).
Enter your answer as a tri-linear inequality accurate to one decimal place (because the sample statistics are reported accurate to one decimal place).

Answer 1

1. The statistical software output for this problem is:

One sample proportion summary confidence interval:
p : Proportion of successes
Method: Standard-Wald

95% confidence interval results:

Proportion	Count	Total	Sample Prop.	Std. Err.	L. Limit	U. Limit
p	140	500	0.28	0.020079841	0.24064424	0.31935576

Hence,

95% confidence interval:

0.241 < p < 0.319

2. The statistical software output for this problem is:

One sample proportion summary hypothesis test:
p : Proportion of successes
H₀ : p = 0.68
H_A : p > 0.68

Hypothesis test results:

Proportion	Count	Total	Sample Prop.	Std. Err.	Z-Stat	P-value
p	314	432	0.72685185	0.022443344	2.0875611	0.0184

Hence,

Test statistic = 2.088

p - Value = 0.0184

The p-value is less than (or equal to) α

Reject the null hypothesis

The sample data support the claim that the proportion of men over 50 who regularly have their prostate examined is more than 0.68.