16. A simple random sample of 28 observations was taken from a large population. The sample mean equaled 50. Fifty is a sample parameter O point estimator point estimate population parameter
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- Suppose θb is an unbiased point estimator for a parameter θ. We obtain 10,000 different random samples and we compute the value of θb every time. Can we say that θb will underestimate θ a total of 5000 times and it will overestimate θ another 5000 times? What do you expect to see in this experiment?If we have a sample of size 100 from a population of rope with sample mean breaking strength of 1040 pounds with standard deviation 200 pounds and we wish to run a hypothesis test with this data to see if the population mean breaking strength exceeds 1000 pounds, what is our ALTERNATE HYPOTHESIS?If the sample data are in the critical region with α = .01, then the same sample data would still be in the critical region if α were changed to .05. True False
- Suppose that 25% of patients with MI in 2000 died within24 hours. This proportion is called the 24-hour case-fatalityrate. Suppose we eventually plan to accumulate 50 MIcases during the period 2010–2015. Assume that the24-hour case-fatality rate is truly 20% during this period.How much power would such a study have in distinguishingbetween case-fatality rates in 2000 and 2010–2015 if atwo-sided test with significance level .05 is planned?Suppose we take a sample of 2,500 blood donors from a population for which 50% (0.5) have type O+ blood. (a) Into what range of possible values should the sample proportion fall 95% of the time, according to the Empirical Rule? to (b) If the sample included only 625 donors instead of 2,500, would the range of possible sample proportions be wider, more narrow, or the same as with a sample of 2,500 donors? Explain your answer, and explain why it makes intuitive sense. The range would be with 625 donors compared to a sample of 2,500 donors since the standard deviation of the sampling distribution would be . This makes intuitive sense because if fewer donors are included in the sample, the proportion will be reliable as an estimate of the proportion.Suppose the average blood sugar level in 35- to 44-year-olds is 4.86 (mmol/L). Do sedentary people have a different blood sugar level than that of the general population? To answer that question, a hypothesis test is planned to collect data from a group of 200 sedentary people in this age group. State the null and alternative hypothesis for this study. A. H0: u (mean) ≠ 4.86 mmol/L vs Ha: u (mean) = 4.86 mmol/L B. H0: u (mean) = 4.86 mmol/L vs Ha: xbar ≠ 4.86 mmol/L C. H0: u (mean) = 4.86 mmol/L vs Ha: u (mean) > 4.86 mmol/L D. H0: u(mean) = 4.86 mmol/L vs Ha: u (mean) ≠ 4.86 mmol/L
- Suppose a study reported that the average persin watched 3.37 hours of television per day. a random sample of 15 people gave the number of hours of television watched per day shown below. at the 1% significance level, do the data provide sufficent evidence to conclude that the amount of television watched per day last year by the average person is greater than the value reported in the study? A.select the correct parameter. a.the average number of hours that all people watch tv b. the average number of hours that the 15 people watch tv c. the fraction of hours people watch tv d. the total number of hours that a person watches tv B. select the correct hypotheses: a. Ho: mu= 3.37 Ha: mu is greater than 3.37 b. Ho: mu=4.103 Ha: mu is greater than 4.103 c.Ho: p=3.37 Ha: p is less than 3.37 d.Ho: mu=3.37 Ha: mu is less than 3.37 C. which of following statements best describes the sampling distribution? a. the sampling distribution is normal with mean 3.37 hours and standard deviation…4. (a) The mean lifetime of 200 mobile phones in a sample is 1,000 hours and their standard deviationis 130 hours. µ is the mean lifetime of all the mobile phones produced. Test the hypothesis thatthe sample comes from a population whose mean is 1,200 hours at 1% significance level?The mean ± 1 SD of calcium intake (in mg) among 25 females, 12-14 years of age, below the poverty level is 6.56 ± 0.64. Similarly, the mean ± 1 SD of calcium intake among 40 females, 12-14 years of age, above the poverty level is 6.80 ± 0.76. Do we have sufficient evidence to conclude that the mean intake of calcium among females below the poverty level is significantly lower than the calcium intake of females above the poverty level? State the null and alternative hypothesis in mathematical notation Ho: Ha: What is the level of significance to be used? What is the appropriate test statistic? Why? What is the critical region? Compute for the test statistic. Show all your computations below. What is the statistical decision? What is your basis for such decision? How would you conclude your findings? Be specific.
- Following an oil spill, a particular region of the ocean is being tested for the level of a chemical called naphthalene. It is considered fact that fish from the region will be safe to eat if, and only if, the mean naphthalene level in the region is less than 3.3 parts per billion. A set of water specimens will be randomly selected from the region and tested, and if the results provide convinving evidence that the mean naphthalene level is less than 3.3, then the sale of fish from the region will be made legal. Which of the following describes a Type I error and its consequences? A) the authorities fail to obtain convincing evidence that the mean naphthalene level is less than 3.3, and do not legalize the sale of fish from the region when in fact the fish are SAFE for consumption. B) The definition of a Type I error depends on the actual results of the study in question C) The authorities fail to obtain convincing evidence that the mean naphthalene level is less than 3.3, and do not…2. The strength of steel wire made by an existing process is normally distributed with a mean of 1550 and a standard deviation of 170. A batch of wire is made by a new process, and a random sample consisting of 25 measurements gives an average strength of 1316. Assume that the standard deviation does not change. Is there evidence at the 1% level of significance that the new process gives a larger mean strength than the old? To answer this question, the alternative hypothesis could be stated as A. µ = 1550 psi B. µ > 1550 psi C. µ ≠ 1550 psi D. µ < 1550 psiSuppose a researcher is interested in the relationship between periodontal disease and a number of negative health outcomes. One outcome of particular interest to the researcher is hypertension (assume defined as systolic blood pressure above 140 mmHG). Suppose a team gathers a SRS of 348 participants with periodontal disease, and finds the sample average systolic blood pressure to be 157 mmHG. A) Using an assumed σ=16 mmHG, conduct a 1 sample Z test to determine if there is a relationship between periodontal disease and hypertension in this population. (Use α=0.05)