Quiz Solutions for STAT 381 - Confidence Intervals and Hypothesis Testing, Quizzes of Data Analysis & Statistical Methods

Download Quiz Solutions for STAT 381 - Confidence Intervals and Hypothesis Testing and more Quizzes Data Analysis & Statistical Methods in PDF only on Docsity! STAT 381 - 13605 Quiz 9 2006-11-22 Solution 1. A tire manufacturer tests n=144 tires and finds their mean life to be x =40,200 miles. The population standard deviation is =σ 1250 miles. Find a 99% confidence interval for the average life of these tires. 1-α = 99%, α = 0.01, α /2= 0.005, then z0.005 = 2.576 ( )3.40468,7.399313.26840200 144 1250576.240200005.0 =±=⎟ ⎠ ⎞ ⎜ ⎝ ⎛ ⋅±=± n zx σ 2. Let Y be a binomial random variable b(n=25, p=0.2), use the normal distribution to approximate the probability )84( ≤≤ YP . Mean μY = np =5, Standard deviation σY = ( ) 28.02.0251 =⋅⋅=− pnp ( ) ( ) ( ) ( )[ ] ( ) 7333.07734.019599.075.075.1 75.175.0 2 55.8 2 55.3 5.85.35.85.3 )5.085.04()84( =−−=−Φ−Φ= ≤≤−=⎟ ⎠ ⎞ ⎜ ⎝ ⎛ −≤≤ − ≅ ⎟⎟ ⎠ ⎞ ⎜⎜ ⎝ ⎛ − ≤ − ≤ − =≤≤= +≤≤−=≤≤ ZPZP YPYP YPYP Y Y Y Y Y Y σ μ σ μ σ μ 3. A telephone company wants to estimate the mean number of minutes people in a city spend talking long distance with 95% confidence. From past records, an estimate of the standard deviation is =σ 12 minutes. What is the minimum sample size required if the desired margin of error is 5 minutes? Confidence 1-α = 95%, α = 0.05, α /2= 0.025, then z0.025 = 1.96 Margin of error B=5 13.22 5 1296.1 2 22 2 22 2/ = ⋅ = ⋅ ≥ B zn σα ↗ 23.