Suppose that a researcher is interested in estimating the mean systolic blood pressure, ????, of executives of major corporations. He plans to use the blood pressures of a random sample of executives of major corporations to estimate ????. Assuming that the standard deviation of the population of systolic blood pressures of executives of major corporations is 24 mm Hg, what is the minimum sample size needed for the researcher to be 99% confident that his estimate is within 5 mm Hg of ????? Carry your intermediate computations to at least three decimal places. Write your answer as a whole number (and make sure that it is the minimum whole number that satisfies the requirements). (If necessary, consult a list of formulas.)
Added by Chloe
Close
Step 1
The problem is asking for the minimum sample size needed to estimate the mean systolic blood pressure of executives of major corporations with a 99% confidence level and a margin of error of 5 mm Hg. The standard deviation of the population is given as 24 mm Hg. Show more…
Show all steps
Your feedback will help us improve your experience
Hoan Nguyen and 58 other Intro Stats / AP Statistics educators are ready to help you.
Ask a new question
Labs
Want to see this concept in action?
Explore this concept interactively to see how it behaves as you change inputs.
Key Concepts
Recommended Videos
19. We wish to design a study to compare two antihypertensive medications. Two outcome variables will be considered: systolic and diastolic blood pressure. a. How many subjects would be required to detect with 80% power and ̑ = 0.05 a difference of 20 units in mean systolic blood pressures between groups? Assume that the standard deviation in systolic blood pressure is 25. b. How many subjects would be required to detect with 80% power and ̑ = 0.05 a difference of 10 units in mean diastolic blood pressures between groups? Assume that the standard deviation in diastolic blood pressure is 21. c. What is the minimum number of subjects we need to satisfy both (a) and (b)? d. Suppose that this study involves enrolling patients and measuring their blood pressures after 6 months—at which time the medications should show an effect. If 10% of the patients drop out of the study within 6 months, how many patients need to be enrolled to satisfy the requirements of (c)? 11. An investigator wished to design a study to estimate the proportion of patients in a particular hospital whose primary insurance coverage is Medicaid. a. How many subjects would be required to estimate the true proportion within 4% with 95% confidence? b. Suppose a similar study was conducted in 2003 and produced the following 95% confidence interval for the proportion of patients in the same hospital whose primary insurance coverage was Medicaid: 27% ± 6%. If the point estimate from the 2003 study is used, how does that affect the answer given in (a)? c. Which answer is more appropriate, (a) or (b)? Be brief.
Shaiju T.
State the hypotheses, determine the model test, state mean std error, analyze the sample data, state the conclusion. Based on this sample result can the researcher conclude that male executives aged 30 to 40 have higher mean systolic blood pressure at a=5%
Ajiboye T.
Please provide the following information. (a) What is the level of significance? State the null and alternate hypotheses. (b) Check Requirements What sampling distribution will you use? Do you think the sample size is sufficiently large? Explain. Compute the value of the sample test statistic and corresponding $z$ value. (c) Find the $P$ -value of the test statistic. Sketch the sampling distribution and show the area corresponding to the $P$ -value. (d) Based on your answers in parts (a) to (c), will you reject or fail to reject the null hypothesis? Are the data statistically significant at level $\alpha$ ? (e) Interpret your conclusion in the context of the application. Medical: Hypertension This problem is based on information taken from The Merck Manual (a reference manual used in most medical and nursing schools). Hypertension is defined as a blood pressure reading over $140 \mathrm{~mm} \mathrm{Hg}$ systolic and/or over $90 \mathrm{~mm}$ Hg diastolic. Hypertension, if not corrected, can cause long-term health problems. In the college-age population (18-24 years), about $9.2 \%$ have hypertension. Suppose that a blood donor program is taking place in a college dormitory this week (final exams week). Before each student gives blood, the nurse takes a blood pressure reading. Of 196 donors, it is found that 29 have hypertension. Do these data indicate that the population proportion of students with hypertension during final exams week is higher than $9.2 \%$ ? Use a $5 \%$ level of significance.
Hypothesis Testing
Testing a Proportion $p$
Recommended Textbooks
Elementary Statistics a Step by Step Approach
The Practice of Statistics for AP
Introductory Statistics
Transcript
Watch the video solution with this free unlock.
EMAIL
PASSWORD