1. The university bookstore claims that the mean cost of textbooks it carries is

Question

1. The university bookstore claims that the mean cost of textbooks it carries is $52 with a standard deviation of $9.50. A group of students want to test this claim. They randomly select 36 textbooks and find that the mean cost for their sample is $55.80. Assuming a .05, is the sample mean cost significantly different from $52? 2. Adult bass in Silver Lake have an average length of 12.3 inches with a standard deviation of 4 inches and a standard error of .3 inches. People who fish often in Silver Lake claim that this year they are catching smaller than usual adult bass. A research group took a random sample of 100 adult bass from Silver Lake and found the mean of this sample to be 11.2 inches. Can the researchers conclude that the fish are smaller than what is normal? Assume a 01 3. AType II error is made when A. we fail to reject the null hypothesis and the null hypothesis is false B. we fail to reject the null hypothesis and the null hypothesis is true C. we reject the null hypothesis and the null hypothesis is false D. we reject the null hypothesis and the null hypothesis is true 4. A Type l error is made when A. we fail to reject the null hypothesis and the null hypothesis is false B. we fail to reject the null hypothesis and the null hypothesis is true C. we reject the null hypothesis and the null hypothesis is false D. we reject the null hypothesis and the null hypothesis is true 5. A researcher is testing a hypothesis of a single mean. The critical z value for a 3.05 and a two-tailed test is t1.96. The calculated test statistic value from sample data is -1.85. The decision made by the researcher based on this information is to A. reject the null hypothesis B. fail to reject the null hypothesis C. redefine the null hypothesis D. change the alternate hypothesis 6. A pharmaceutical company claims that its weight loss drug allows women to lose on average 8.5lb after one month of treatment. If we want to conduct an experiment to determine if the patients are losing less weight than advertised, which of the following hypotheses should be used? A. Ho: us 8.5; H1: 8.5 B. Ho: H 8.5; H1: 8.5 C. Ho: 8.5; H1: 8.5 D. Ho: u z 8.5; H1: H. 8.5 7. A school counselor randomly selects a sample of 30 students to investigate the impact of a behavior intervention on their academic performance. If she increases her sample size to 50 she will the statistical power of her study A. increase

Explanation / Answer

(1)

Data:     

n = 36    

= 52    

s = 9.5    

x-bar = 55.8    

Hypotheses:    

Ho: = 52    

Ha: 52    

Decision Rule:    

= 0.05    

Lower Critical z- score = -1.959963985   

Upper Critical z- score = 1.959963985   

Reject Ho if |z| > 1.959963985   

Test Statistic:    

SE = s/n = 9.5/36 = 1.583333333   

z = (x-bar - )/SE = (55.8 - 52)/1.58333333333333 = 2.4

p- value = 0.016395072    

Decision (in terms of the hypotheses):   

Since 2.4 > 1.959963985 we reject Ho and accept Ha

Conclusion (in terms of the problem):

There is sufficient evidence that the mean is different from 52.   

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