An Omaha electronics firm has received a shipment of 200 special components desi

Question

An Omaha electronics firm has received a shipment of 200 special components designed to maintain a constant power output, 64 watts, with a standard deviation of 4 watts. A sample of 36 of these components produced an average of 64.8 watts. The firm is interested in knowing, at the 02 significance level, if the manufacturer's claim of 64 watts is true. 2. What type of hypothesis test is this (two-tailed, lower or upper tail)? State null and alternative hypotheses. a. b. Use the level of significance (a) to determine the "critical value" (cut-off point), draw on a distribution c. What does the level of significance mean in this problem? d. Compute the test statistic e. Make a decision: Accept or Reject He f. Interpret your decision

Explanation / Answer

Given that,
population mean(u)=64
standard deviation, =4
sample mean, x =64.8
number (n)=36
null, Ho: =64
alternate, H1: !=64
level of significance, = 0.02
from standard normal table, two tailed z /2 =2.326
since our test is two-tailed
reject Ho, if zo < -2.326 OR if zo > 2.326
we use test statistic (z) = x-u/(s.d/sqrt(n))
zo = 64.8-64/(4/sqrt(36)
zo = 1.2
| zo | = 1.2
critical value
the value of |z | at los 2% is 2.326
we got |zo| =1.2 & | z | = 2.326
make decision
hence value of |zo | < | z | and here we do not reject Ho
p-value : two tailed ( double the one tail ) - ha : ( p != 1.2 ) = 0.23
hence value of p0.02 < 0.23, here we do not reject Ho
ANSWERS
---------------
a.
our test is two-tailed
b.
critical value: -2.326 , 2.326
c.
level of significance, = 0.02
d.
test statistic: 1.2
e.
decision: do not reject Ho
p-value: 0.23
f.
we don't have evidence to support the manufacturers claim of 64 watts is true

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