In a random sample of seven medium-sized bags of redi-mix concrete, the mean wei

Question

In a random sample of seven medium-sized bags of redi-mix concrete, the mean weight was 14.38 kg with a sample standard deviation of 1.47 kg. Assume that the weights of bags of redi-mix concrete are normally distributed. (a) If you wish to test the claim that the mean weight of medium-sized bags of redi-mix is less than 15 kg, what should the null hypothesis and alternative hypothesis be? (b) Using a 0.05 significance level to test the claim, (i) find the value of the test statistic, and its P-value. (ii) find the critical region for the test statistic. (c) What do you conclude?

Explanation / Answer

Given that,
population mean(u)=15
sample mean, x =14.38
standard deviation, s =1.47
number (n)=7
null, Ho: >15
alternate, H1: <15
level of significance, = 0.05
from standard normal table,left tailed t /2 =1.943
since our test is left-tailed
reject Ho, if to < -1.943
we use test statistic (t) = x-u/(s.d/sqrt(n))
to =14.38-15/(1.47/sqrt(7))
to =-1.116
| to | =1.116
critical value
the value of |t | with n-1 = 6 d.f is 1.943
we got |to| =1.116 & | t | =1.943
make decision
hence value of |to | < | t | and here we do not reject Ho
p-value :left tail - Ha : ( p < -1.1159 ) = 0.15358
hence value of p0.05 < 0.15358,here we do not reject Ho
ANSWERS
---------------
null, Ho: =15
alternate, H1: <15
test statistic: -1.116
critical value: -1.943
decision: do not reject Ho
p-value: 0.15358

we have enough evidence to support it is less than 15

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