An automobile mileage study tested the following hypotheses.HypothesisConclusionHo: 4 2 25 mpg Manufacturer's claim supportedHạ: µ < 25 mpgManufacturer's claim rejected;average mileage per gallon less than statedFor o = 3 and a .02 level of significance, what sample size would be recommended if the researcher wants an 80% chance ofdetecting that u is less than 25 miles per gallon when it is actually 24 (to the next whole number)?

Power given power of a test we have to find the sample size.

Answered: An automobile mileage study tested the…

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 automobile mileage study tested the following hypotheses. Hypothesis Conclusion H0: µ 25 mpg Manufacturer’s claim supported Ha: µ 25 mpg Manufacturer’s claim rejected; average mileage per gallon less than stated For σ 3 and a .02 level of significance, what sample size would be recommended if the researcher wants an 80% chance of detecting that µ is less than 25 miles per gallon when it is actually 24?
Is there a significant difference in the unemployment rates among Hispanic and white adults in the state of Texas? Based on data collected by the Texas Workforce Commission, 4.6% of 640 randomly selected Hispanic adults are unemployed while 2.8% of 780 randomly selected white adults are unemployed. Does this data provide statistically significant evidence that there is a difference in the unemployment rates between the two groups? a) State the null hypothesis (H0) and the alternative hypothesis (Ha ) for the significance test and the conditions b) assume the conditions are satisfied, identify the test statistic (z or t?) to be used, and show the formula for the test statistic, and enter the appropriate values in the formula. (don’t calculate the test statistic here.) c) Assume that the standard error of the differences in proportions is SE = 0.00995. Using this SE, calculate the value of the test statistic (which you set up in part (b) and find the p-value d) Using a significance…
A well-known brokerage firm executive claimed that 40% of investors are currently confident of meeting their investment goals. An XYZ Investor Optimism Survey, conducted over a two week period, found that in a sample of 500 people, 35% of them said they are confident of meeting their goals.Test the claim that the proportion of people who are confident is smaller than 40% at the 0.005 significance level.The null and alternative hypothesis would be: H0:μ≥0.4 H1:μ<0.4 H0:p≤0.4 H1:p>0.4 H0:p=0.4 H1:p≠0.4 H0:p≥0.4 H1:p<0.4 H0:μ=0.4 H1:μ≠0.4 H0:μ≤0.4 H1:μ>0.4 The test is: two-tailed left-tailed right-tailed The test statistic is: (to 3 decimals)The p-value is: (to 4 decimals)Based on this we: Reject the null hypothesis Fail to reject the null hypothesis
. The term sample usually refers to a sample that ___ - Consists of people with chemical dependency problems - Uses the same group of individuals with a before/after measurement - Requires a dependent variable for hypothesis testing - Is randomly selected from two dependent populations
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When asked what it means for the result of a hypothesis test to be practically significant (or practically important), Tatum says this means that the P-value is small and the null hypothesis has been rejected. Why is Tatum wrong?
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A biologist was interested in determining whether specific seedlings treated with a new fertilizer resulted in a higher than average height than the standard height of 11.2 cm. The biologist treated a random sample of 24 seedlings with the fertilizer and subsequently obtained the following heights. Conduct an appropriate hypothesis test using a 5% significance level. What is the null and alternative hypothesis? What is the value of the test stastic? Please show work. 11.5 11.8 15.7 12.1 10.1 10.5 16.5 13.5 14.4 16.7 10.9 10.0 11.1 17.1 13.3 12.4 8.5 14.3 12.9 11.1 15.0 13.3 9.9 13.5
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A veterinarian is interested in researching the proportion of men and women cat owners and believes that the proportion of men cat owners is significantly different than the proportion of women cat owners. The veterinarian decides to obtain two independent samples of men and women cat owners and finds from one sample of 80 men, 30% owned cats. In the second sample of 60 women, 55% owned cats. Test the veterinarian's belief at the α=0.05α=0.05 significance level. Preliminary: Is it safe to assume that nmen≤5%nmen≤5% of all men and nwomen≤5%nwomen≤5% of all women? Yes No Verify nˆp(1−ˆp)≥10.np^(1-p^)≥10. Round your answer to one decimal place.nmenˆp(1−ˆp)=nmenp^(1-p^)= nwomenˆp(1−ˆp)=nwomenp^(1-p^)= Test the claim: Determine the null and alternative hypotheses. H0H0: pmenpmen pwomenpwomen HaHa: pmenpmen pwomenpwomen The hypothesis test is left-tailed two-tailed right-tailed Determine the test statistic. Round to two decimal places.x=x= Find the pp-value.…
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.

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