Chapter 8 – Hypothesis Testing

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1 Suppose that the average song length in America is 4 minutes with a standard deviation of 1.25 minutes. It is known that song length is not normally distributed. Find the probability that a single randomly selected song from the population will be longer than 4.25 minutes. Round to the nearest thousandth. Answer A. 0.579 B. 0.079 C. 0.421 D. This probability cannot be determined because we do not know the distribution of the population. 2 An outcome of an experiment or study that is large enough to have a real effect on people’s health or lifestyle is said to have clinical significance. Answer True False 3 Are average SAT scores higher in schools where a smaller percentage of graduating students take the test? To answer this question 10 schools are sampled and the average SAT and percentage of students taking the test were recorded. 2002 SAT results of regional high schools were sampled and the data is given below. Use that data to test if there is a relation between the proportion of seniors that take the test and the average SAT scores. At 95% confidence level. 2002 SAT results of a sample of Western North Carolina High Schools. Mean SAT scores 1106 1040 1013 1066 1061 1075 1058 997 1014 965 Percent tested 61 59 44 54 72 74 80 32 49 What is R2 for the equation? A. R2=0.793 B.B. R2= 0.429 C. C. R2=0.326 D. D. R2=0.357 4. Suppose the Acme Drug Company develops a new drug, designed to prevent colds. The company states that the drug is equally effective for men and women. To test this claim, they choose a simple random sample of 100 women and 200 men from a population of 100,000 volunteers. At the end of the study, 38% of the women caught a cold; and 51% of the men caught a cold. State the null and alternative hypothesis: Answer A. H0: p1 = p2 : HA: p1 = p2 : B. H0: p1 < p2 HA: p1< p2 : C. H0: p1 > p2 HA: p1> p2 : D. H0: p1 ≠ p2 HA: p1= p2 : 5 An insurance company is reviewing its current policy rates. When originally setting the rates they believed that the average claim amount was $1,800. They are concerned that the true mean is actually higher than this, because they could potentially lose a lot of money. They randomly select 40 claims, and calculate a sample mean of $1,950. Assuming that the standard deviation of claims is $500, and set α = 0.05, test to see if the insurance company should be concerned. What do we interpret from the problem? Answer A. P value < α so we reject Ho B. P value > α so we do not reject Ho C. P value < α so we do not reject Ho D. P value < α so we reject Ho 6 1. To achieve a significance level of α, if the p-value is less than (or equal to) α, then________________ Answer A. accept the null hypothesis B. do not reject the null hypothesis C. reject the null hypothesis D. accept the alternative hypothesis 7 1. Neuroscience researchers examined the impact of environment on rat development. Rats were.

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Hypothesis Testing Definitions: A statistical hypothesis is a guess about a population parameter. The guess may or not be true. The null hypothesis, written H0, is a statistical hypothesis that states that there is no difference between a parameter and a specific value, or that there is no difference between two parameters. The alternative hypothesis, written H1 or HA, is a statistical hypothesis that specifies a specific difference between a parameter and a specific value, or that there is a difference between two parameters. Example 1: A medical researcher is interested in finding out whether a new medication will have undesirable side effects. She is particularly concerned with the pulse rate of patients who take the medication. The research question is, will the pulse rate increase, decrease, or remain the same after a patient takes the medication? Since the researcher knows that the mean pulse rate for the population under study is 82 beats per minute, the hypotheses for this study are: H0: µ = 82 HA: µ ≠ 82 The null hypothesis specifies that the mean will remain unchanged and the alternative hypothesis states that it will be different. This test is called a two-tailed test since the possible side effects could be to raise or lower the pulse rate. Notice that this is a non directional hypothesis. The rejection region lies in both tails. We divide the alpha in two and place half in each tail. Example 2: An entrepreneur invents an additive to increase the life of an automobile battery. If the mean lifetime of the automobile battery is 36 months, then his hypotheses are: H0: µ ≤ 36 HA: µ > 36 Here, the entrepreneur is only interested in increasing the lifetime of the batteries, so his alternative hypothesis is that the mean is greater than 36 months. The null hypothesis is that the mean is less than or equal to 36 months. This test is one-tailed since the interest is only in an increased lifetime. Notice that the direction of the inequality in the alternate hypothesis points to the right, same as the area of the curve that forms the rejection region. Example 3: A landlord who wants to lower heating bills in a large apartment complex is considering using a new type of insulation. If the current average of the monthly heating bills is $78, his hypotheses about heating costs with the new insulation are: H0: µ ≥ 78 HA: µ < 78 This test is also a one-tailed test since the landlord is interested only in lowering heating costs. Notice that the direction of the inequality in the alternate hypothesis points to the left, same as the area of the curve that forms the rejection region. Study Design: After stating the hypotheses, the researcher’s next step is to design the study. In designing the study, the researcher selects an appropriate statistical test, chooses a level of significance, and formulates a plan for conducting the study..

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