Question

On average, a banana will last 6.3 days from the time it is purchased in the store to the time it is too rotten to cat Is the mean time to spoil less if the banana is hung from the ceiling? The data show results of an experiment with 13 bananas that are hung from the ceiling. Assume that that distribution of the population is normal 1,4,45,47,72,3.6,54,55,52,56,5.6,63,6.2 What can be concluded at the the a -0.05 level of significance level of significance? a. For this study, we should use Select an answer b. The null and alternative hypotheses would be c. The test statistic d. The p-value = e. The p-value is ? f Based on this, we should Select an answer g Thus, the final conclusion is that (please show your answver to 3 decimal places) (Please show your answer to 4 decimal places) the null hypothesis. The data suggest the population mean is not significantly less than 6 3 at a-o 05, so there is statistically insignificant evidence to conclude that the population mean time that at takes for bananas to spoul if they are hung from the cesling is equal to 6.3 The data suggest that the population mean time that it takes for bananas to spoil if they are hung from the ceiling is not significantly less than 6 3 at o 005, so there is statistically insignificant evidence to conclude that the population mean time that it takes for bananas to spoil if they are hung fron the cesling is less than 63 The data suggest the populaton mean ıs significantly less than 6 3 ar α-o 05, so there is statistically significant evidence to conclude that the population mean time that st takes for bananas to spoil if they ar hing from the cealing is less than 6.3 638PM

Answer 1

Given that,
population mean(u)=6.3
sample mean, x =5.2231
standard deviation, s =1.0248
number (n)=13
null, Ho: μ=6.3
alternate, H1: μ<6.3
level of significance, alpha = 0.05
from standard normal table,left tailed t alpha/2 =1.782
since our test is left-tailed
reject Ho, if to < -1.782
we use test statistic (t) = x-u/(s.d/sqrt(n))
to =5.2231-6.3/(1.0248/sqrt(13))
to =-3.789
| to | =3.789
critical value
the value of |t alpha| with n-1 = 12 d.f is 1.782
we got |to| =3.789 & | t alpha | =1.782
make decision
hence value of | to | > | t alpha| and here we reject Ho
p-value :left tail - Ha : ( p < -3.7889 ) = 0.00129
hence value of p0.05 > 0.00129,here we reject Ho
ANSWERS
---------------
a.
t test for single mean is used.
b.
null, Ho: μ=6.3
alternate, H1: μ<6.3
c.
test statistic: -3.789
d.
critical value: -1.782
f.
decision: reject Ho
e.
p-value: 0.00129
g.
we have enough evidence to support the claim that population mean is significantly less than 6.3