Probability should be rounded to 4 decimal places. Mean and standard deviations
ID: 3130763 • Letter: P
Question
Probability should be rounded to 4 decimal places. Mean and standard deviations to 2 decimal places.
Chapter 5 (Normal Distributions # 1-3)
4.) The following data are the calories per half-cup serving for 16 popular chocolate ice cream brands. 300 350 275 180 260 395 185 195 260 170 160 290 170 180 225 145 Estimate the true mean calories per half-cup serving of chocolate ice cream with 90% confidence. To Earn FULL credit, Include an interpretation statement with your answer. (Section 6.2) Chapter 7 (Hypothesis Test #7 - 8) – Show all steps – See page 357 for list of steps - for each hypothesis test in order to earn FULL credit.
5.) A medical researcher wishes to determine the percentage of females who take vitamins. He wishes to be 95% confident that the estimate is within 2.35 percentage points of the true proportion. A recent study of 315 females showed that 68% took vitamins. How large should the sample size be?
Explanation / Answer
4.
Note that
Lower Bound = X - t(alpha/2) * s / sqrt(n)
Upper Bound = X + t(alpha/2) * s / sqrt(n)
where
alpha/2 = (1 - confidence level)/2 = 0.05
X = sample mean = 233.75
t(alpha/2) = critical t for the confidence interval = 1.753050356
s = sample standard deviation = 73.6319677
n = sample size = 16
df = n - 1 = 15
Thus,
Lower bound = 201.4798632
Upper bound = 266.0201368
Thus, the confidence interval is
( 201.4798632 , 266.0201368 ) [ANSWER]
Hence, we are 90% confident that the true mean calories per half-cup serving of chocolate ice cream is between 201.4798632 and 266.0201368. [CONCLUSION]
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