a)In a random sample of 20 second year statistics students from a normal distribution, N(μ, 0²)selected by a lecturer, found thatb)Σ₁X₁ = 30 and 2₁X² = 60.Zi=1i) If the lecturer assumes that μ = 2, what is her 90% two sided confidence interval for o²?ii) If the lecturer assumes that μ is unknown, what will be her 90% two sided confidence intervalfor o²?iii) Would you accept Ho: o² = 1 against Ho: o² # 1 in each case, i) and ii)? Explain.Suppose that X₁, X2, ..., Xn denotes a random samples from a gamma distribution f(x; α, ß).i) What will be the minimal sufficient statistic for ß? Explain.2¹X¹ is a pivotal quantity.Bii) If a = 2, use the appropriate method to show that Y =iii) Given that a random sample of heavy machines from Polokwane factory produced thefollowing noise levels 85.4, 86.8, 86.1, 85.3 and 84.8. Use part ii) of question 3 b) to constructa 95% confidence interval for B.

It is given that Sample size n = 20 ∑X = 30 , ∑X2 = 60 Note : Since you have asked multiple…

Answered: a) In a random sample of 20 second year…

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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3. Assume that the distribution of the length X of male spider is N(ux,o}) and the length Y of female spiders is N(µy,o?), and X and Y are independent. Construct approximated 95% one-sided confidence intervals for o? /o? when n = m = 30, and = 0.4399 and S? = 1.4100.
4. The lower value of a 90% confidence interval for the variance in maze-running times of a sample of 31 rats is 4.62. Based on this, form a 98% confidence interval for 02 Answer: 3.973 to 13.5219
From a random sample of 100 women, 15 have dangerous reading blood sugar levels higher than 300 mg/dL. The 95% confidence interval for the proportion of all women with dangerous reading levels is O a. 0.15+ (1.96) √0.1275 O b. O d. 0.15 0.15 (1.6449) √0.0013 (1.6449) √0.1275 0.15 (1.96) √0.0013
A nutritionist took a random sample of 60 college students at Harvard and made a 95% confidence interval for the average calories consumed in a day. The interval that the researcher obtained was 2350 to 2620. A) about 95% of the population of students at Harvard is between 2350 and 2620, true or false? B) if the nutritionist had taken a sample of 100 college students. Would the 95% confidence interval with n= 100 be wider or narrower than the 95% confidence interval with n= 60 students?
) A random sample of size n = 6 is selected from a normal population, with 12) the sample variance s? = .18. Determine a confidence interval for the population variance o? with a confidence level of 98 percent.
The results of a mathematics exam at JUST university for two classes are as follows: Class 1: (n=32 , mean=12.6, SD=8) and Class 2: (n=36, mean=2.4, SD=12).we are testing if the means are different What is the z statistic (a=0.05): on О а. 1.7000 O b. 6.1237 O c. 3.7559 O d. 4.1641
Assume that both populations are normally distributed. a) Test whether . Population 1 Population 2 10 11.1 Pt2 at the a= 0.05 level of significance for the given sample data 10 9.8 2.3 (b) Construct a 95% confidence interval about u, - H3. 2.7 H1 H1 > H2 O C. Ho H1-H2 H1 H1> H2 D. Ho H1=H2 %3D Detemine the P-value for this hypothesis test. P = (Round to three decimal places as needed.) %24
A simple random sample of size n=17 is drawn from a population that is normally distributed. The sample mean is found to be x= 69 and the sample standard deviation is found to be s= 20. Construct a 95% confidence interval about the population mean. ..... The lower bound is The upper bound is
7) A group of 39 randomly selected students have a mean score of 19.5 with a standard deviation of 3.2 on a placement test. What is the 99% confidence interval for the mean score, μ, of all students taking the test? O 27.9 μ< 31.9 O 18.2 μ< 20.8 28.2 μ< 30.8 O 18.1 μ< 20.9
M, SMz 4. The results of a taste test between competing soda brands Cola A and Cola B are presented below. Two independent random samples were selected and the respondents rated the colas on a scale of 1 to 10. Cola A: sample size = 38, sample mean =7.92, sample standard deviation = 2.9 Cola B: sample size = 45, sample mean = 7.22, sample standard deviation = 1.4 Construct a 95% confidence interval for the difference between the average ratings for Cola A and Cola B. State your conclusion in terms of the problem. 2.9 95,37 2,03 14
b )part?
b) The following table gives the weekly sales of hand gloves for a random sample of 40 weeks in store A: Sales (pairs) Number of weeks 30 -< 40 1 40 - < 50 3 50 - < 60 8 60 -< 70 12 70 -< 80 80 - < 90 3 90 -< 100 4 Construct a 95% confidence interval for the population proportion of weeks having sales at least 80 pairs.

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