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In: Statistics and Probability

Identify the null and alternative hypothesis(in symbolic and sentence form), test statistic, P-value(or critical values), conclusion...

Identify the null and alternative hypothesis(in symbolic and sentence form), test statistic, P-value(or critical values), conclusion about the null hypothesis, and final conclusion that addresses the original claim (Don’t just say Reject the null hypothesis or fail to reject the null hypothesis).

5. A simple random sample of 15-year old boys from one city is obtained and their weights (in pounds) are listed below. Use a 0.01 significance level to test the claim that these sample weights come from a population with a mean equal to 147 lb. Assume that the standard deviation of the weights of all 15-year old boys in the city is known to be 16.7 lb.

146 140 160 151 134 189 157 144 175 127 164

Solutions

Expert Solution

5.

Given that,
population mean(u)=147
standard deviation, σ =16.7
sample mean, x =153.3636
number (n)=15
null, Ho: μ=147
alternate, H1: μ!=147
level of significance, α = 0.01
from standard normal table, two tailed z α/2 =2.576
since our test is two-tailed
reject Ho, if zo < -2.576 OR if zo > 2.576
we use test statistic (z) = x-u/(s.d/sqrt(n))
zo = 153.3636-147/(16.7/sqrt(15)
zo = 1.476
| zo | = 1.476
critical value
the value of |z α| at los 1% is 2.576
we got |zo| =1.476 & | z α | = 2.576
make decision
hence value of |zo | < | z α | and here we do not reject Ho
p-value : two tailed ( double the one tail ) - ha : ( p != 1.476 ) = 0.14
hence value of p0.01 < 0.14, here we do not reject Ho
ANSWERS
---------------
null, Ho: μ=147
alternate, H1: μ!=147
test statistic: 1.476
critical value: -2.576 , 2.576
decision: do not reject Ho
p-value: 0.14
we do not have enough evidence to support the claim that these sample weights come from a population with a mean equal to 147 lb.

orchestra answered 1 year ago
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