Q 20. Let u be the mean serum cholesterol level of the population of 20- to 74-year-old males in a particular countryμand we wish to test the null hypothesis Ho:μ ≥ 220mg/100ml at the significance level a = 0.05. We knowthat the standard deviation of the population is o = 60mg/100ml, and the true population mean is as smallas 200mg/100ml.(a) Find the minimum sample size we need so that the power of the test can be at least 95%. (10 marks)(b) If the true population mean is 180mg/100ml instead of 200mg/100ml, describe how the significancelevel and power will be affected, i.e., increased, decreased or unchanged. Justify your answer. (6 marks)(c) If we decrease the significance level, will the power of test be increased? Justify your answer. (4 marks)(20 marks)

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Answered: Q 20. Let µ be the mean serum…

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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17. A 20,000-piece manufacturing run of 2200 resistors has a mean value of 2200 (naturally!) and a standard deviation of 2.50. They are to be sold as a 2% tolerance product, which means that the values must be between 0.98 x220 N = 215.60 and 1.02 x 220 0 = 224.40.
You need to test whether the average mealtime spending of American tourists (population 1) is greater than that for British tourists (population 2). Assume that you have a sample of n1=7 with sample mean X1=40 and a sample standard deviation of S1=6, and you have an independent sample of n2=16 from another population with a sample mean of X2=31 and sample standard deviation S2=5. Complete parts (a) to (d). Click here to view page 1 of the table of the critical values of t. LOADING... Click here to view page 2 of the table of the critical values of t. LOADING... a. What is the value of the pooled-variance t test statistic for testing? t=enter your response here (Type an integer or a decimal rounded to two decimal places as needed.) b. In finding the critical value of the test statistic t, how many degrees of freedom are there? There are enter your response here degrees of freedom. c. Using a significance level of α=0.01, what is the critical value for a…
The American Milk Association is claiming that men drink more milk than women. If a sample of 45 men drink on average 26 oz of milk a day with a standard deviation of 5oz. A sample of 40 women drink on average 24oz of milk a day with a standard deviation of 3oz. At the .10 significance level using (z or t value of 2.26), can we conclude that men drink more milk than women? Group of answer choices REJECT Ho; We CANNOT prove the claim that Men drink more milk than Women. DO NOT REJECT Ho; We CAN prove the claim that Men drink more milk than Women. REJECT Ho; We CAN prove the claim that Men drink more milk than Women. DO NOT REJECT Ho; We CANNOT prove the claim that Men drink more milk than Women. Flag this Question
A nutritionist claims that the mean tuna consumption by a person is 3.6 pounds per year. A sample of 70 people shows that the mean tuna consumption by a person is 3.4 pounds per year. Assume the population standard deviation is 1.19 pounds. At alphaαequals=0.05, can you reject the claim? (a) Identify the null hypothesis and alternative hypothesis. A. Upper H 0H0: muμless than or equals≤3.6 Upper H Subscript aHa: muμgreater than>3.6 B. Upper H 0H0: muμgreater than>3.6 Upper H Subscript aHa: muμless than or equals≤3.6 C. Upper H 0H0: muμnot equals≠3.4 Upper H Subscript aHa: muμequals=3.4 D. Upper H 0H0: muμgreater than>3.4 Upper H Subscript aHa: muμless than or equals≤3.4 E. Upper H 0H0: muμequals=3.6 Upper H Subscript aHa: muμnot equals≠3.6 F. Upper H 0H0: muμless than or equals≤3.4 Upper H Subscript aHa: muμgreater than>3.4 (b) Identify the standardized test statistic.…
IQ is known to be normally distributed with a mean of 100 and standard deviation of 16. A small school of 64 students has a mean IQ of105. What is the approximate value of the test statistic associated with this sample mean and what conclusion should be drawn in relation to the overall population? z = +2.5; reject H0 and conclude that this sample is significantly higher in IQ than the general population t = -0.27; retain H0 and conclude that the IQ for this sample is not significantly different from the general IQ population z = +2.0; retain H0 and conclude that the IQ for this sample is not significantly different from the general IQ population z = +2.5; retain H0 and conclude that the IQ for this sample is not significantly different from the general IQ population
In 2019, the average SAT score in New York State was 1,064 with a standard deviation of 175. Solve for X using z-values obtained from Microsoft Excel and the Area Under the Curve Table. Population Mean, μ, = 1,064 Population Standard Deviation, σ, 175 X = μ + zσ What SAT score do you need to be among the top 0.5 percent? X μ z-value σ z = NORM.S.INV(0.995) 1,064 175 z w/Excel 1,064 175 Area Under the Curve Table What SAT score do you need to be among the top 2.5 percent? X μ z-value σ z = NORM.S.INV(0.975) 1,064 175 z w/Excel 1,064 175 Area Under the Curve Table What z-value is the cut-off point for the bottom 10 percent? X μ z-value σ z = NORM.S.INV(0.1) 1,064 175 z w/Excel 1,064 175 Area Under the Curve Table What z-value is the cut-off point for the bottom 1 percent? X μ z-value σ z = NORM.S.INV(0.01)…
The null and alternate hypotheses are:H0: μ₁ = μ2H1: μ₁ ≠ μ2 A random sample of 10 observations from one population revealed a sample mean of 26 and a sample standard deviation of 5.0. A random sample of 8 observations from another population revealed a sample mean of 30 and a sample standard deviation of 6.0. The population standard deviations are unknown but assumed to be equal. At the 0.01 significance level, is there a difference between the population means?
3.1. Suppose that the height of the women is a normal variable with a mean of 1.62 meters (m) and a standard deviation of 24 centimeters. Calculate the percentage of women who measures (a) more than 1.70 m. (b) between 1.66 and 1.58 m. (c) less than 1.50 m. d) between 1.60 and 1.63 m.
Assume that the readings at freezing on a batch of thermometers are normally distributed with a mean of 0°C and a standard deviation of 1.00°C. A single thermometer is randomly selected and tested. Let ZZ represent the reading of this thermometer at freezing. What reading separates the highest 39.28% from the rest? That is, if P(z>c)=0.3928 find c.
2. It assumed that the maximum temperature in Oman is normally distributed with a mean of 9 and a standard deviation of 9/2 for which: P(9 − a ≤ X ≤ 9 + a) = 0.5934. calculate the value of “ a “.
Suppose now that that Y denotes the annual salaries (in thousands of dollars) for US citizenswho are in their 40s and 50; and X is an indicator (dummy) variable: X = 1 if that workergraduated from college and X=0 otherwise. Suppose the average annual salary for this age groupis $45,000 and the estimate for β is β~ = 15 with s.e. = 5.a. What is the t-statistic and associated p-value for the null hypothesis that attending collegehas no impact on subsequent salary?b. What is the upper and lower bound of a 95-percent confidence interval for β~ ?c. In a credible research design attending college would be randomly assigned to a largesample of potential students. Propose such a research design. What are the potential ethicalissues?
To obtain information on the corrosion-resistance properties of a certain type of steel conduit, 45 specimens are buried in soil for a 2-year period. The maximum penetration (in mils) for each specimen is then measured, yielding a sample average penetration of x = 53.7 and a sample standard deviation of s = 4.3. The conduits were manufactured with the specification that true average penetration be at most 50 mils. They will be used unless it can be demonstrated conclusively that the specification has not been met. What would you conclude? (Use ? = 0.05.)State the appropriate null and alternative hypotheses. H0: ? = 50Ha: ? ≠ 50H0: ? = 50Ha: ? > 50 H0: ? ≠ 50Ha: ? > 50H0: ? > 50Ha: ? = 50 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. Reject the null hypothesis. There is sufficient evidence to…

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