QRMFINAL

QRMFINAL - HAT CAN NEVER BE NEGATIVE OR GREATER THAN ONE IN...

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$C$2:$E$38 $B$2:$B$38 xXXX t (df) THAT CAN NEVER BE NEGATIVE OR GREATER THAN ONE IN VALUE. ALWAYS INFINITY ( ) PART I. HYPOTHESIS TESTING PROBLEM 1 A certain brand of fluorescent light tube was advertised as having an effective life span before burning out of 4000 hours. A random sample of 84 bulbs was burned out with a mean illumination life span of 1870 hours and with a sample standard deviation of 90 hours. Construct a 95 confidence interval based on this sample and be sure to interpret this interval. Solution: Here n = 84, Mean x = 1870, Standard Deviation s = 90 α = 95%, so Z α = 1.96 Confidence interval = x ± Z α × sn = 1870 ± 1.96 × (90/ 84) = 1870 ± 19.2468 = (1870-19.2468, 1870 + 19.2468) = (1850.7532, 1889.2468) The 95 percent confidence interval is (1850.7532, 1889.2468) Interpretations: We are 95 percent confident that the true mean illumination life span is within the interval 1850.7532 < μ < 1889.2468. There is a 95 percent chance that an interval constructed in this manner contains μ (but a 5 percent chance that it does not).
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PROBLEM 2 Given the following data from two independent data sets, conduct a one-tail hypothesis test to determine if the means are statistically equal using alpha=0.05. Do NOT do a confidence interval. n 1 = 35 n 2 = 30 xbar 1 = 32 xbar 2 = 25 s 1 =7 s 2 = 6 Step 1: Null hypothesis: H 0 : Alternate hypothesis: H 0 : Step 2: For α = .05 in a left-tailed test, the critical value is z .05 =− 1.645, so the decision rule is Reject H 0 if z < 1.645 Otherwise do not reject H 0 Step 3: Identify the test statistic Z = Step 4: Make the Decision Since the test statistic does not fall in the rejection region, we do not reject the null hypothesis Step 5: interpretation 2
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Thus we conclude that the means are not statistically equal PROBLEM 3. A test was conducted to determine whether gender of a display model affected the likelihood that consumers would prefer a new product. A survey of consumers at a trade show which used a female spokesperson determined that 120 of 300 customers preferred the product while 92 of 280 customers preferred the product when it was shown by a female spokesperson. Do the samples provide sufficient evidence to indicate that the gender of the salesperson affect the likelihood of the product being favorably regarded by consumers? Evaluate with a two-tail, alpha =.01 test. Do NOT do a confidence interval. 3
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suming that the population variances are equal for Male and Female GPA’s, test the following sample data to see if Male and Female PhD candidate GPA’s (Means ) are equal. Conduct a two-tail hypothesis test at α =.01 to determine whether the sample means are different. Do NOT do a confidence interval. Male GPA’s
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QRMFINAL - HAT CAN NEVER BE NEGATIVE OR GREATER THAN ONE IN...

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