A bank manager wants to know the mean amount of mortgage paid per month by homeo
ID: 3336668 • Letter: A
Question
A bank manager wants to know the mean amount of mortgage paid per month by homeowners in an area. A random sample of 112 homeowners selected from this area showed that they pay an average of $1570 per month for their mortgages. The population standard deviation of such mortgages is $216.
b. Suppose the confidence interval obtained in part a is too wide. Select all of the ways the width of this interval can be reduced.
A bank manager wants to know the mean amount of mortgage paid per month by homeowners in an area. A random sample of 112 homeowners selected from this area showed that they pay an average of $1570 per month for their mortgages. The population standard deviation of such mortgages is $216.
Explanation / Answer
Mean is 1570 and s is 216. the standard error SE is s/sqrt(N)=216/sqrt(112) =20.41
a) For 95% confidence, the z value is 1.96, the lower limit thus is mean-SE*z=1570-20.41*1.96=1529.996
upper limit is mean+SE*z=1570+20.41*1.96 =1610.0036
b) if the sample size is lowered, the width of interval increases. if the confidence interval is increased, the width increases, thus to reduce the width, option s B and D are correct
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