i) Derive the standard error of ß, se(B) = 0.0009, using MLE approach. ii) Find an approximate 95% Confidence interval for B.
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Q: b) Find the critical value of t for a 90% confidence interval with df=58.
A: It is given that,Confidence level Degrees of freedom To find the critical t value.
![c)
Let Y₁, Y₂,..., Yn be a random sample whose probability density function is given by
f(v:B)= 684
- fa
0<y<∞ and ß>0
0,
elsewhere
200
200
200
and suppose that n = 200, y = 20, y = 100, y = 250 and $ = 0.025.
i=1
i) Derive the standard error of ß, se(B) = 0.0009, using MLE approach.
ii) Find an approximate 95% Confidence interval for B.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F59fc304e-f174-4073-beaa-c91da01ee65e%2Fb8c02aab-f067-48af-8108-b83649a6e16a%2Fzc5ymsc_processed.jpeg&w=3840&q=75)
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Firstly it is required to determine the MLE of the parameter and then the variance to get the required confidence interval.
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- The recommended daily dietary allowance for zinc among males older than age 50 years is 15 mg/day. An article reports the following summary data on intake for a sample of males age 65−74 years: n = 116, x = 12.5, and s = 6.35. Does this data indicate that average daily zinc intake in the population of all males age 65−74 falls below the recommended allowance? (Use ? = 0.05.)State the appropriate null and alternative hypotheses. H0: ? = 15Ha: ? ≠ 15H0: ? = 15Ha: ? > 15 H0: ? = 15Ha: ? ≤ 15H0: ? = 15Ha: ? < 15 Calculate the test statistic and determine the P-value. (Round your test statistic to two decimal places and your P-value to four decimal places.) z = P-value = State the conclusion in the problem context. Do not reject the null hypothesis. There is not sufficient evidence that average daily zinc intake falls below 15 mg/day.Reject the null hypothesis. There is not sufficient evidence that average daily zinc intake falls below 15 mg/day. Do not reject…T/F: An R^2 value near 100% indicates that there is a strong causal relationship between the response and the predictor variables. T/F: Standard deviation of the sum of two independent random variables is the sum of their standard deviations.11% of all Americans suffer from sleep apnea. A researcher suspects that a different percentage of those who live in the inner city have sleep apnea. Of the 344 people from the inner city surveyed, 34 of them suffered from sleep apnea. What can be concluded at the level of significance of αα = 0.01? The test statistic= (please show your answer to 3 decimal places.) The p-value = (Please show your answer to 4 decimal places.)
- A random sample of 82 eighth grade students' scores on a national mathematics assessment test has a mean score of 286. This test result prompts a state school administrator to declare that the mean score for the state's eighth graders on this exam is more than 280. Assume that the population standard deviation is 38. At α = 0.05, is there enough evidence to support the administrator's claim? Complete parts (a) through (e). (a) Write the claim mathematically and identify Ho and H₂. Choose the correct answer below. O A. Ho: ≤280 (claim) H₂:μ>280 O D. Ho: μ≤280 Ha: μ> 280 (claim) B. Ho: μ280 OF. Ho: μ = 280 H₂: µ>280 (claim)Heart rates are determined before and 30 minutes after a Kettleball workout. It can be assumed that heart rates (bpm) are normally distributed. Use the data provided below to test to determine if average heart rates prior to the workout are significantly lower than 30 minutes after a Kettleball workout at the 0.02 level of significance. Let μ₁ = mean before workout. Select the correct Hypotheses: Ho:με 2 με Η: μι = με Η: μη μ₂ O O O Conclusion: before 69 69 65 62 63 61 after 73 75 72 70 68 59 O Fail to Reject Ho ● Reject Ho Test Statistic = p-value = Ho:μd = 0 H₁: Hd ‡0 O [three decimal accuracy] [three decimal accuracy] Ho:μα 20 Ha:Pa 0 O Interpret the conclusion in context: ● There is enough evidence to suggest the mean bpm before a Kettleball workout is lower than 30 minutes after the workout. O There is not enough evidence to suggest the mean bpm before a Kettleball workout is lower than 30 minutes after the workout.You are conducting a study to see if the proportion of women over 40 who regularly have mammograms is significantly less than 0.24. Thus you are performing a left-tailed test. Your sample data produce the test statistic z=−2.665z=-2.665. Find the p-value accurate to 4 decimal places.
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- The herbal supplement ginkgo biloba is advertised as producing an increase in physical strength and stamina. To test this claim, a sample of n = 120 adults is obtained and each person is instructed to take the regular daily dose of the herb for a period of 30 days. At the end of the 30 days each person is tested on a standard treadmill task for which the average age-adjusted score is μ = 15. The individuals in the sample produce a mean score of M = 17.4 with SS = 1260. Are these data sufficient to conclude that the herb had a statistically significant effect? Conduct as a two-tailed test, using all hypothesis steps with p < .05. BONUS POINTS: Calculate the 95% confidence intervalYou are conducting a study to see if the proportion of women over 40 who regularly have mammograms is significantly less than 0.66. Thus you are performing a left-tailed test. Your sample data produce the test statistic z=−1.812z=-1.812. Find the p-value accurate to 4 decimal places.Researchers wish to investigate whether anxiety in children has increased over time. In 1950, the average score on the Child Manifest Anxiety Scale was µ= 15.1. A sample of n = 16 was taken from children today, which produced a mean anxiety score of M= 23.3 with SS= 240. Based on the sample, has there been a significant change in the average level of childhood anxiety since 1950? (Use a 2-tailed test with α= .05) Write a sentence describing the outcome of the hypothesis test as it would appear in a research report.
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