Problem #2 Show:Step 1: State the hypothesisStep 2: The level of significance and critical regionStep 3: Compute for the valueStep 4: Decision ruleStep 5: Conclusion1. Average Senior High School annual cost oftuition fee for all private schools last year wasP46,300. A random sample of costs this year for45 private schools indicated that the sample meanwas P47,800 and a sample standard deviation wasP5,600. At the 0.10 level of significance, is theresufficient evidence to conclude that the cost hasincreased?2. A report in LTO stated that the average age oftaxis in the Philippines is 12 years. An operationsmanager of a large taxi company selects a sampleof 40 taxis and finds the average age of the taxis is11.2 years. The standard deviation of thepopulation is 2.3 years. At 0.05 level ofsignificance, can it be concluded that the averageage of the taxis in his company is less than thenational average?

It is given that Sample size n = 40 Sample mean M = 11.2 Population SD = 2.3 Level of significance =…

Answered: significance, can it be concluded that…

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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An investigator hypothesizes that the improvement rate associated with a placebo is P1 = 0.45, and that the improvement rate associated with an active drug is P2 = 0.65. The plan is to perform a two-tailed test. Use SAS to complete each problem below. (a) If a significance level 0.01 and a power of 0.95 are desired, how large a sample per treatment must he study? (b) How large must the sample size be if the significance level is relaxed to 0.05 and the power to 0.85? (c) For this study, suppose that you have funds to recruit 130 patients per group. What is the power for a 5% level test for this sample size? First do the computation by hand and then use SAS to confirm.
Given a sample mean of 94.3, a sample standard deviation of 8.4 and a sample size of 6,test the hypothesis that the value of the population mean is 100 against the alternativehypothesis that it is less than 100. Use the 0.05 significance level.
A) Given the significance level α=0.06 find the following: (a) left-tailed zz valuez= (b) right-tailed z valuez= (c) two-tailed zz value|z|= B) Golf-course designers have become concerned that old courses are becoming obsolete since new technology has given golfers the ability to hit the ball so far. Designers, therefore, have proposed that new golf courses need to be built expecting that the average golfer can hit the ball more than 250 yards on average. Suppose a random sample of 184184 golfers be chosen so that their mean driving distance is 252.7 yards, with a population standard deviation of 42 Conduct a hypothesis test where H0:μ=250 and H1:μ>250 by computing the following:(a) test statistic (b) p-value -HypothesisTests
2.1 The operations manager of a motor vehicle accessories firm with branches in Limpopo and Durban wants to establish whether their Limpopo branch is performing better than their Durban branch in terms of the average size of orders received. Both branches have been operating for only one year. A random sample of 31 orders from the Limpopo branch had an average value of R355.20 with a standard deviation equal to R151.50. Orders received by the Durban branch of the firm were also randomly sampled. The average of the 35 orders sampled was R265.60 with a sample standard deviation of R162.20. Can the operations manager conclude, at the 3% significance level, that the Limpopo branch is performing better than the Durban branch? Show the null and alternative hypotheses for the test and draw the appropriate conclusion. Compute the p-value.
On Excel spreadsheet, find the results of the hypothesis test for the equality of the mean production levels between the two locations Tampa, Florida, and Columbus, Ohio. The current production goals for the monthly production level of the cases are a mean of at least 1,000 units per month and a standard deviation of less than 100 units per month. Are the company goals being met for the cases produced at the Tampa, Florida location? Are the company goals being met for the cases produced at the Columbus, Ohio location? Are the mean production levels the same between the Tampa, Florida and Columbus, Ohio locations?
1.The sports equipment company developed a synthetic type of fishing line which is claimed to have an average strength of 8 kg and a standard deviation of 0.5 kg. It is known that with a sample of 50 synthetic fishing rods the average strength is 7 kg. With a significance level of 0.01, Test the hypothesis that the population mean is really equal to 8 kg
If we were to ask for a minimum sample size for a 94% level of confidence what would the value for z-sub-c be?
An investigator hypothesizes that the improvement rate associated with a placebo is P1 = 0.45, and that the improvement rate associated with an active drug is P2 = 0.65. The plan is to perform a two-tailed test. Use SAS to complete each problem below. (b) How large must the sample size be if the significance level is relaxed to 0.05 and the power to 0.85? Suppose that instead of accruing an equal number of patients on each treatment arm, you allocate 1.5 patients to the new treatment for every patient on standard treatment. What sample size is required on each arm to guarantee 85% power with a level 0.05? How does the sample size computed here compare with the total required sample size in (b)?
(Follow the steps in Test of Hypothesis and include your conclusion) Two suppliers manufacture a plastic gear used in a laser printer. The impact strength of these gears measures in foot-pounds is an important characteristic. A random sample of 10 gears from supplier 1 results in x1 = 290 and s1 = 12 while another random sample of 16 gears from the second supplier results in x2 = 321 and s2 = 22. Is there evidence to support the claim that supplier 2 provides gears with higher mean impact strength. Use a =0.04, and assume that both populations are normally distributed with equal variances.
Question 20. part C. Nationally, patients who go to the emergency room wait an average of 7 hours to be admitted into the hospital. Do patients at rural hospitals have a lower waiting time? The 14 randomly selected patients who went to the emergency room at rural hospitals waited an average of 5.8 hours to be admitted into the hospital. The standard deviation for these 14 patients was 1.7 hours. What can be concluded at the the αα = 0.05 level of significance level of significance? F.) Based on this, we should Select an answer accept, reject or fail to reject the null hypothesis? G.) Thus, the final conclusion is that ... (Which one) The data suggest the populaton mean is significantly lower than 7 at αα = 0.05, so there is statistically significant evidence to conclude that the population mean waiting time to be admitted into the hospital from the emergency room for patients at rural hospitals is lower than 7 hours. The data suggest the population mean is not significantly lower…
Sample surveys conducted in a large county in a cer-tain year and again 20 years later showed that originally the average height of 400 ten-year-old boys was 53.8inches with a standard deviation of 2.4 inches, whereas20 years later the average height of 500 ten-year-old boyswas 54.5 inches with a standard deviation of 2.5 inches.Use the four steps in the initial part of Section 1 andthe 0.05 level of significance to test the null hypothesisμ1 − μ2 = −0.5 against the alternative hypothesis μ1 −μ2 < −0.5.
A sample of 100 observations has a sample mean of 500 and a sample standard deviation of 50. Conduct a hypothesis test to determine if the population mean is equal to 480 at a significance level of 0.05.

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significance, can it be concluded that the average age of the taxis in his company is less than the national average?