The quality-control manager at a compact fluorescent light bulb (cfl) factory needs to determine whether the mean life of a large shipment of cfls is equal to 7450 hours. the population standard deviation is 1 comma 350 hours. a random sample of 81 light bulbs indicates a sample mean life of 7 comma 240 hours. a. at the 0.05 level of significance, is there evidence that the mean life is different from 7450 hours question mark b. compute the p-value and interpret its meaning. c. construct a 95% confidence interval estimate of the population mean life of the light bulbs. d. compare the results of (a) and (c). what conclusions do you reach

Let be the population mean .

By observing the given information, we have :-

Since the alternative hypotheses is two tailed so the test is a two-tailed test.

We assume that the  life of a large shipment of CFLs is normally distributed.

(a) Given : Sample size :  n=81 , since n>30 so we use z-test.

Sample mean :

Standard deviation :

Test statistic for population mean :-

The critical value (two-tailed) corresponds to the given significance level :-

Since the observed value of z (-1.4) is less than the critical value (1.96) , so we do not reject the null hypothesis.

Hence, we conclude that we have enough evidence to accept that the mean life is different from 7450 hours .

(b) The p-value : , it means that the probability that the life of CFLs less than 7240 and greater than 7240 is 0.1615.

(c) The confidence interval for population mean is given by :-

,

the smallest possible measurement of the width is 14 feet

step-by-step explanation:

let's assume length of parallelogram is 'l'

width of parallelogram is 'w'

the perimeter of a parallelogram must be no less than 40 feet

so, we get

we are given

length of parallelogram is 6 feet

so,

l=6

we can plug it

now, we can solve for w

subtract both sides by 12

divide both sides by 2

and we get

so,

the smallest possible measurement of the width is 14 feet

answer: yard ramps with a level off platform are typically 36 feet long. truck, rather than at an angle, enabling access to those pallets at the very back of the truck. if you are using your yard ramp to convert a loading dock into a drive-in door, we even at 60 inches (5 feet) high and a 30 foot ramp, the slope of the ramp will be less

step-by-step explanation: