Question

A fluorescence probe can be used to label cell nuclei. The cell incubation time needed for the fluorescence probe to label the cell nuclei is an important consideration in the experimental protocol. If the mean incubation time is longer that 1.5 hour, the fluorescence probe will not be suitable for the experimental protocol. Twenty cells cultures are selected, and their reported minimum required incubation time (in hours) are as follows: 1.6, 1.3, 1.5, 1.6, 1.7, 1.9, 1.8, 1.6, 1.4, 1.8, 1.9, 1.8, 1.7, 1.5, 1.6, 1.4, 1.3, 1.6, 1.5, and 1.8. Would you recommend the fluorescence probe for the experimental protocol?

Answer 1

Given that,
population mean(u)=1.5
sample mean, x =1.615
standard deviation, s =0.179
number (n)=20
null, Ho: μ=1.5
alternate, H1: μ>1.5
level of significance, α = 0.05
from standard normal table,right tailed t α/2 =1.729
since our test is right-tailed
reject Ho, if to > 1.729
we use test statistic (t) = x-u/(s.d/sqrt(n))
to =1.615-1.5/(0.179/sqrt(20))
to =2.8732
| to | =2.8732
critical value
the value of |t α| with n-1 = 19 d.f is 1.729
we got |to| =2.8732 & | t α | =1.729
make decision
hence value of | to | > | t α| and here we reject Ho
p-value :right tail - Ha : ( p > 2.8732 ) = 0.00487
hence value of p0.05 > 0.00487,here we reject Ho
ANSWERS
---------------
null, Ho: μ=1.5
alternate, H1: μ>1.5
test statistic: 2.8732
critical value: 1.729
decision: reject Ho
p-value: 0.00487
we have enough evidence to support the claim that If the mean incubation time is longer that 1.5 hour.
yes,
recommend the fluorescence probe for the experimental protocol