Question

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). If you used the calculator, identify everything mentioned above in addition to which calculator functions and inputs for each field were used.

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

Answer #1

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

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please upvote

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