**Probability and Sampling in Healthcare Studies**According to *Reader's Digest*, 30% of primary care doctors believe their patients receive unnecessary medical care. The analysis below uses the z-table to answer related statistical inquiries.### TaskSuppose a sample of 400 primary care doctors is taken to analyze the proportion of doctors who think their patients receive unnecessary medical care.1. **Expected Value and Standard Error** - Calculate the expected sample proportion \( E(\hat{p}) \). - Determine the standard error \( \sigma_{\hat{p}} \). Fill in: - \( E(\hat{p}) = \_\_\_ \) (to 2 decimals) - \( \sigma_{\hat{p}} = \_\_\_ \) (to 4 decimals)2. **Probability Within Tolerance** - **b.** What is the probability that the sample proportion is within \(\pm 0.03\) of the population proportion? Round your answer to four decimals.3. **Probability with Larger Tolerance** - **c.** What is the probability that the sample proportion is within \(\pm 0.05\) of the population proportion? Round your answer to four decimals.4. **Effect of a Larger Sample** - **d.** Discuss the effect of increasing the sample size on the probabilities in parts (b) and (c). The probabilities would: [Select your answer]. Explain why: Increasing the sample size decreases the standard error, \( \sigma_{\hat{p}} \). [Select your answer].---This exercise facilitates a deeper understanding of how sample size affects precision and the probability of achieving results within a specified tolerance of the population proportion in statistical studies.

As per our guidelines, we are allowed to answer first three sub-parts only . Thanks Given : p = 0.3…

Answered: According to Reader's Digest, 30% of…

MATLAB: An Introduction with Applications

6th Edition

ISBN:9781119256830

Author:Amos Gilat

Publisher:Amos Gilat

Chapter1: Starting With Matlab

Section: Chapter Questions

Problem 1P

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d. Give a 95% interval estimate of the number of fatal accidents per 1000 licenses in a city where 15% of the licensed drivers are under 21.
Refer to the figure at the right. At a =0.10, can you reject the claim that the proportion of 18 to 24-year-olds living in their parents' homes in 2000 was the same for men and women? Assume the survey included a random sample of 248 men and 244 women. Percentage of 18-to 24-year olds living in parents' homes 70- 51.5% 41.2% 46.6% 44.3% 0- 2012 I Women 2000 Men Identify the null and alternative hypotheses. Choose the correct answer below. O A. Ho: P1 #P2 Ha: P1 = P2 O B. Ho: P, P2 c. Họ: P1 = P2 Ha: P1 #P2 O D. Ho: P1 >P2 Ha: P1 SP2 Find the critical value(s). The critical value(s) is(are) ±1.65. (Round to two decimal places as needed. Use a comma to separate answers as needed.) Find the standardized test statistic. (Round to two decimal places as needed.)
The table to the right is based on the assumption that 1% of breast tumors are malignant. It also assumes that mammogram screening is 90% accurate. Complete parts (a) through (c) below. Positive Mammogram Negative Mammogram Total % (Type an integer or decimal rounded to the nearest tenth as needed.) b. What is the chance of a positive mammogram, given that the patient has cancer? % (Type an integer or decimal rounded to the nearest hundredth as needed.) Tumor is Tumor is Malignant Benign 90 1206 a. Suppose a patient has a positive mammogram. What is the chance that she really has cancer? 10 100 8694 9900 % (Type an integer or decimal rounded to the nearest tenth as needed.) c. Suppose a patient has a negative mammogram. What is the chance that she actually does have cancer? Total 1296 8704 10,000
Refer to the figure at the right. At a = 0.10, can you reject the claim that the proportion of 18 to 24-year-olds living in their parents' homes in 2000 was the same for men and women? Assume the survey included a random sample of 270 men and 278 women. Percentage of 18- to 24-year olds living in parents' homes 70,60.4% 54.6% 50.3% 45% 2000 2012 I Men IWomen Identify the null and alternative hypotheses. Choose the correct answer below. O B. Ho: P1 + P2 A. Ho: P1= P2 Hg: P1 P2 H: P1 =P2 OD. Ho: P,> P2 OC. Ho: P1 P2 Hg: P, SP2 Find the critical value(s). The critical value(s) is(are) +1.65. (Round to two decimal places as needed. Use a comma to separate answers as needed.) Find the standardized test statistic. z= 3.61 (Round to two decimal places as needed.) Can you reject the claim that the proportion of 18 to 24-year-olds living in their parents' homes was the same for men and women in 2000? . at the 10% significance level, there is v evidence to v the claim.
Refer to the figure at the right. At a =0.10, can you reject the claim that the proportion of 18 to 24-year-olds living in their parents' homes in 2000 was the same for men and women? AsSsume the survey included a random sample of 248 men and 244 women. Percentage of 18- to 24-year olds living in parents' homes 70,. 51.5% 41.2% 46.6% 44.3% 2000 2012 O Men Women Identify the null and alternative hypotheses. Choose the correct answer below. O A. H,: P, +P2 Ha: P1 = P2 O B. Ho: P, P2 c. Họ: P1 = P2 O D. Ho: P1 > P2 Ha: P, SP2 Ha: P1 #P2 Find the critical value(s). The critical value(s) is(are) +1.65 (Round to two decimal places as needed. Use a comma to separate answers as needed.) Find the standardized test statistic. z= 2.29 (Round to two decimal places as needed.) Can you reject the claim that the proportion of 18 to 24-year-olds living in their parents' homes was the same for men and women in 2000? V, at the 10% significance level, there is evidence to the claim.
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Refer to the figure at the right. At a =0.10, can you reject the claim that the proportion of 18 to 24-year-olds living in their parents' homes in 2000 was the same for men and women? Assume the survey included a random sample of 248 men and 244 women. Percentage of 18- to 24-year olds iving in parents' homes 7051.5% 41.2% 46.6% 44.3% 2000 2012 I Men I Women Identify the null and alternative hypotheses. Choose the correct answer below. O B. Ho: P1 P2 O D. Ho: P, > P2 Cc. Họ: P1 = P2 Ha: P, SP2 H3: P, *P2 Find the critical value(s). The critical value(s) is(are) +1.65. (Round to two decimal places as needed. Use a comma to separate answers as needed.) Find the standardized test statistic. z= 2.29 (Round to two decimal places as needed.) Can you reject the claim that the proportion of 18 to 24-year-olds living in their parents' homes was the same for men and women in 2000? Yes , at the 10% significance level, there is sufficient evidence to support the claim.
Suppose that out of 10,351 convicts who escaped from U.S. prisons, only 7767 were recaptured. Let p represent the proportion of all escaped convicts who will eventually be recaptured. Find a point estimate for p. Round your answer to four decimal places.
John works as a weld inspector in a shipyard. Because he keeps track of good and poor welds, he knows that 5% of all welds will be poor during the afternoon shift. What are the chances that the proportion of poor welds will be more than 0.083 based on a sample of 300 welds? O a 0.0044 Ob 0.9957 Ⓒc 0.0045 Od 0.9881
The correlation between midterm and final grades for 300 students is 0.620. If 5 points are added to each midterm grade, the new r will be: a. 0.124 b. 0.57 c. 0.62 d. 0.744
Suppose that insurance companies did a survey. They randomly surveyed 400 drivers and found that 310 claimed they always buckle up. We are interested in the population proportion of drivers who claim they always buckle up. Which distribution should you use for this problem? (Round your answer to four decimal places.)
Use the figure to the right, which shows the percentages of adults from several countries who favor building new nuclear power plants in their country. The survey included random samples of 1051 adults from Country A, 1120 adults from Country B, 1048 adults from Country C, and 1013 adults from Country D. At a =0.05, can you support the claim that the proportion of adults in Country B who favor building new nuclear power plants in their country is different from the proportion of adults from Country C who favor building new nuclear power plants in their country? Assume the random samples are independent. 100- 80- 60 40 20- 0- I Country A 53% I Country B 47% O Country C 46% O Country D 34% Identify the claim and state Ho and Ha. The claim is "the proportion of adults in Country B who favor building new nuclear power plants in their country is the same as the proportion of adults from Country C who favor building new nuclear power plants in their country." greater than less than different…

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