Follow the 6-step Hypothesis Testing Method and make sure to show All steps. 1)
ID: 3222206 • Letter: F
Question
Follow the 6-step Hypothesis Testing Method and make sure to show All steps.
1) A nationwide study of American homeowners revealed that 64% have one or more lawn mowers. A lawn equipment manufacturer, located in Omaha, feels that the estimate is too low for households in Omaha. Can the claim of 0.64 be rejected if a survey of 490 homes in Omaha yields 331 with one or more lawn mowers? Use a 0.05 significance level.
2) Assume that the sample has been randomly selected from a population with a normal distribution. A seismologist takes a random same of earthquake depths and finds the following summary statistics. n=50 and xbar1=9.81 km. The seismologist wants to test the claim that these earthquakes are from a population with a mean depth equal to 10 km. Assume that the population standard deviation is 5.01 km.
Explanation / Answer
Given that,
possibile chances (x)=331
sample size(n)=490
success rate ( p )= x/n = 0.6755
success probability,( po )=0.64
failure probability,( qo) = 0.36
null, the estimate is too low for households in Omaha Ho:p<=0.64
alternate, H1: p>0.64
level of significance, = 0.05
from standard normal table,right tailed z /2 =1.64
since our test is right-tailed
reject Ho, if zo > 1.64
we use test statistic z proportion = p-po/sqrt(poqo/n)
zo=0.67551-0.64/(sqrt(0.2304)/490)
zo =1.6376
| zo | =1.6376
critical value
the value of |z | at los 0.05% is 1.64
we got |zo| =1.638 & | z | =1.64
make decision
hence value of |zo | < | z | and here we do not reject Ho
p-value: right tail - Ha : ( p > 1.63761 ) = 0.05075
hence value of p0.05 < 0.05075,here we do not reject Ho
ANSWERS
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null, Ho:p<=0.64
alternate, H1: p>0.64
test statistic: 1.6376
critical value: 1.64
decision: do not reject Ho
p-value: 0.05075
we have evidence to support the claim