Question

A company that produces cell phones claims its standard phone battery lasts longer on average than other batteries in the market. To support this​ claim, the company publishes an ad reporting the results of a recent experiment showing that under normal​ usage, their batteries last at least 34 hours. To investigate this​ claim, a consumer advocacy group asked the company for the raw​ data, which are shown to the right. Find a 90​% confidence interval and state your conclusion. Explain how you dealt with any outliers. Time 30, 31, 32, 34, 32, 32 / 31, 32, 34, 56, 31, 33 1. Find the confidence interval usisng all the data (Round to two decimal places) 2. if outliers are present, find the confidence interval without the outlier ( Round to two decimal places)

Answer 1

90% confidence interval for population mean life of cellphone battery n = 12 sample size x6bar = 34 hours sample mean s = 7.0324hours sample standard Deviation (Standard deviation is found using Excel function stdev s (data)) Confidence interval for mean is given by x^bar plusminus Z * s/squareroot n For 90 % alpha = 0.10 alpha/2 = 0.05 From the Z - table, or Excel Funtion NORM.S INV (alpha/2) z = NORM > S > INV (0.5) = 1.645 (We take the positive value for calculations) x^bar plsuminus Z * sigma squareroot n = 34 plusminus 1.645 * 7.024/squareroot 12 = (30.6605, 37,3395) = (30.66,37.34) Rounded to 2 decimal places 90% confidence interval for mean life of cellphone battery is (30.66,37.34) hours To find outiers, we find the quartiles Q_1,Q_3 and inter quartile Range IQR using Excel function we find the Q_1 and Q_2 Q_1 = QUARTILE. INC (data,1) Q-1 = 31 Q_3 = QUARTILE.IN (data,1) Q3 = 33.25 IQR = Q3 - Q1 = 33.25 - 31 = 2.25 1.5IQR = 1.5 * 2.25 = 3.375