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(Solved) Biostatistics 100A Dr. M. Lee Spring, 2016 Midterm #2 (100 pts) ANSWERS Name: UCLA ID: (2 pts ea) 1. In testing H0: = 120 with = .05 and n = 50 (ONLY...

Can you please help me with Question number 2? I don't know which equations or logic to use to solve this problem

Biostatistics 100A

Dr. M. Lee Spring, 2016 Midterm #2 (100 pts)

ANSWERS

Name: UCLA ID: (2 pts ea) 1. In testing H0: Âµ = 120 with Î± = .05 and n = 50 (ONLY ONE RIGHT ANSWER)

a. If n is changed to 100 and Î± is left unchanged, what happens to Î²?

(increased, decreased, remains unchanged)

DECREASED b. If n is changed to 25 and Î± is left unchanged, what happens to

1-Î²? (increased, decreased, remains unchanged)

DECREASED c. If Î± is changed to .01 and n is left unchanged, what happens to Î²?

(increased, decreased, remains unchanged)

INCREASED d. If H0 is false, but the true Âµ is actually very close to 120, Î² will be very

close to: 0, 1, 0.5

1 e. If H0 is false, but the true Âµ is actually very far from 120, 1-Î² will be very

close to: 0, 1, 0.5

1 2. An industrious Biostatistics 100A student decides to compute a confidence

interval for the mean daily fat intake of UCLA students. As such, she takes a

sample of 49 students and obtains x-bar = 25g and assumes Ïƒ = 14g. The

interval was then calculated and the result was:

21.72 < Âµ< 28.28 (14 pts) a. What level of confidence was used? ANSWER IS APPROXIMATELY 90%. (5 pts) b. In computing this interval we (choose all that are correct):

(i) required a random sample of students (ii) assumed the distribution of fat intake was normal (iii) used the Central Limit Theorem (iv) did not require the normal distribution (10 pts) c. If we had wanted the margin of error of this interval to be 0.82, what

sample size should we have used to achieve the same level of confidence

that was used in part a.? n = (1.64 x sigma/margin)2 = (1.64 x 14/0.82)2 = 784 (6 pts) d. Assume for the purposes of just this portion of the problem that the

confidence level of the interval given in part a is 99%, then which of the

following statements are correct? (More than one may be correct)

(i) P(Âµ < 21.72) = .005 (ii) P(21.72 < Âµ < 28.28) = .99 (iii) If we were to take another sample from this population, we would

probably get an interval with the same endpoints. (iv) The probability is 1% that if we were to take another sample, the

new x-bar would be smaller than 21.72 or larger than 28.28. (v) The formula that generated the interval in question yields a correct

statement (contains Âµ) 99% of the time. (vi) If we were to take another sample from this population but the

sample size was 100, the resulting interval would be narrower

compared to the current one. 3. A recent medical article stated that the average person with migraines suffers

with about 15 headaches per year. An enterprising public health student

decides to test that claim and selected a sample of 4 migraine sufferers. The

number of headaches they reported was:

7, 10, 12, 15

At the 5% level of significance, is it possible to conclude that the articleâ€™s claim

is incorrect?

Answer the following: (5 pts) a. Hypotheses

H0: Âµ=15

THIS IS WORTH 2 POINTS

H1: Âµâ‰ 15

THIS IS WORTH 3 POINTS; -1 FOR A ONE-SIDED HYPOTHESIS (5 pts) b. Assumptions (circle all that apply)

(i) Simple random sample of migraine sufferers (ii) Normal distribution of glasses of number of headaches per year (iii) Central Limit Theorem applies (iv) Population standard deviation known (5 pts) c. Decision rule

REJECT H0 IF T > 3.182 OR < -3.182 (5 pts) d. Calculations (value of test statistic) T = (11-15)/(3.37/SQRT(4)) = -2.37 (5 pts) e. Statistical decision FAIL TO REJECT H0 (4 pts) f. Depending on your statistical decision, what type of statistical error could

you possibly have made? Î² ERROR. 4. True or False (2 pts. each) T F a. The smaller the level of confidence, the shorter the confidence interval. T F b. For a fixed confidence level, when the sample size increases, the margin

of error of the confidence interval for a population mean decreases T F c. The null hypothesis, H0, is considered correct until proven otherwise. T F d. If the null hypothesis is rejected, this means that the alternative hypothesis

must be true. T F e. As the sample size increases, Î²-error decreases. T F f. Î² = 1-Î± T F g. If we reject H0, then we say we have conclusively proven that H 1, is true. T F h. If we take a large enough sample from any population, then the histogram

for the sample data could not be skewed. T F I. If we take a large random sample, the mean of the sample will be

approximately equal to the median. T F j. If we reject H0 at Î± = .05, the probability is 0.95 that H1 is correct. 5. Assume that a null hypothesis for a statistical test is true. Say whether each of

following statements is true or false: (2 points each)

a. Calculating the p-value assumes that sample is a random sample. TRUE

b. If you reject H0 with a hypothesis test, you will be making a Type II error.

FALSE

c. If you fail to reject H0 with a hypothesis test, you will be making a Type 1

error. FALSE

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