## MS Mod 4 pps mcq type 1 and type 2 errors practice exam questions

 Author Message NEAS Supreme Being         Group: Administrators Posts: 4.2K, Visits: 1.2K MS Module 4 pps mcq type 1 and type 2 errors practice exam questions(The attached PDF file has better formatting.)A population has a normal distribution with a mean μ0 of 60 and a standard deviation of 7.3One group from this population has been treated to reduce its mean; we assume it is still normally distributed with the same standard deviation. A sample of size 22 from this treated group has a sample mean of and a true mean of μʹ.●    The null hypothesis is H0: μʹ = μ0.●    The one-sided alternative hypothesis is Ha: μʹ < μ0.We reject the null hypothesis if ≤ 58.8Question 1.2: Standard deviation of sample meanWhat is the standard deviation of the sample mean?Answer 1.2: 7.3 / 220.5 = 1.556(standard deviation of the sample mean = standard deviation / (number of observations in sample)0.5 )Question 1.3: z statisticWhat is the z statistic value to test the null hypothesis?Answer 1.3: (58.8 – 60) / 1.556 = -0.771(the z statistic value to test the null hypothesis = (sample mean – mean assumed in null hypothesis (μ0) ) / standard deviation of the sample mean)Question 1.4: Probability of Type I errorWhat is the probability of a Type I error for this one-sided (lower-tailed) test?Answer 1.4: Φ(–0.771) = 0.2203Interpolating in the statistical tables: Φ(0.77) = 0.7794Φ(0.78) = 0.7823Φ(–0.771) = 1 – ( (0.771 – 0.77) × 0.7823 + (0.78 – 0.771) × 0.7794) / (0.78 – 0.77) = 0.2203Question 1.5: Probability of Type II errorIf the true mean of the sample μʹ is 59.3 , what is the probability of a Type II error for this test?Answer 1.5: (59.3 – 58.8) / 1.556 = 0.3213, so Φ(59.3 – 58.8) / 1.556 = Φ(0.3213) = 0.6260Interpolating in the statistical tables: Φ(0.32) = 0.6255Φ(0.33) = 0.6293Φ(0.3213) = ( (0.3213 – 0.32) × 0.6293 + (0.33 – 0.3213) × 0.6255) / (0.33 – 0.32) = 0.6260 Attachments MS Module 4 pps mcq type 1type 2 errors practice exam questions.pdf (240 views, 44.00 KB)
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