Collette is self-employed, selling items at Home Interior parties. She wants to
ID: 3081083 • Letter: C
Question
Collette is self-employed, selling items at Home Interior parties. She wants to estimate the average amount a client spends at each party. A random sample of 35 clients' receipts gave a sample mean of $34.70. This historical population standard deviation of her party sales is $4.85. a).Should you use the critical value (zc) or (tc) in determining a confidence interval in this problem? Explain. b)Find a 90% confidence interval for the average amount expected to be spent by an individual. c).Write a brief expanation of the meaning of the confidence interval in the context of this problem d).For a party with 35 clients, use part (b) to estimate a range of dollar values for Collette's total sales at that party.Explanation / Answer
ANSWER: An additional 97 students needed since Sample Size = 147 is necessary for 99% level of confidence. Why??? SMALL SAMPLE, LEVEL OF CONFIDENCE, NORMAL POPULATION DISTRIBUTION Margin of Error (half of confidence interval) = 1 The margin of error is defined as the "radius" (or half the width) of a confidence interval for a particular statistic. Level of Confidence = 99 s: population standard deviation = 4.7 ('z critical value') from Look-up Table for 99% = 2.576 The Look-up in the Table for the Standard Normal Distribution utilizes the Table's cummulative 'area' feature. The Table shows positve and negative values of ('z critical') but since the Standard Normal Distribution is symmetric, the magnitude of ('z critical') is important. For a Level of Confidence = 99% the corresponding LEFT 'area' = 0.495. And due to Table's symmetric nature, the corresponding RIGHT 'area' = 0.495 The ('z critical') value Look-up is 2.576 which means the MIDDLE 'area' = SUM[LEFT 'area' + RIGHT 'area'] for a Level of Confidence = 99. significant digits = 3 Margin of Error = ('z critical value') * s/SQRT(n) n = Sample Size Algebraic solution for n: n = [('z critical value') * s/Margin of Error]² = [ (2.576 * 4.7)/1 ]² Sample Size = 147 for 99% level of confidence