Mathematics, 08.04.2020 03:35 danny223

Ask Your Teacher A journal article reports that a sample of size 5 was used as a basis for calculating a 95% CI for the true average natural frequency (Hz) of delaminated beams of a certain type. The resulting interval was (229.266, 233.002). You decide that a confidence level of 99% is more appropriate than the 95% level used. What are the limits of the 99% interval? [Hint: Use the center of the interval and its width to determine x and s.] (Round your answers to three decimal places.)

Answers: 2

Show answers

Answers

Answer from: genyjoannerubiera

The 99% confidence interval is (228.035, 234.233).

Step-by-step explanation:

The sample size selected to compute the 95% confidence interval for the true average natural frequency (Hz) of delaminated beams of a certain type is

n = 5

The sample size is very small and the population standard deviation is also not known.

So, we will use t-interval for the confidence interval.

The (1 - α)% confidence interval for the true mean is:

$CI=\bar x\pm t_{\alpha/2, (n-1)}\times \frac{s}{\sqrt{n}}$

The 95% confidence interval for the true average natural frequency (Hz) of delaminated beams of a certain type is:

(Upper limit, Lower limit) = (229.266, 233.002).

Compute the value of sample mean as follows:

$\bar x=\frac{UL+LL}{2}=\frac{233.002+229.266}{2}=231.134$

The critical value of t for α = 0.05 and n = 5 is:

$t_{\alpha/2, (n-1)}=t_{0.05/2, (5-1)}=t_{0.025,4}=2.776$

*Use a t-table.

Compute the value of sample standard deviation as follows:

$\frac{UL-LL}{2}=t_{\alpha/2, (n-1)}\times \frac{s}{\sqrt{n}}\\\frac{233.002-229.266}{2}=2.776\times\frac{s}{\sqrt{5}}\\s=1.505$

The critical value of t for α = 0.01 and n = 5 is:

$t_{\alpha/2, (n-1)}=t_{0.01/2, (5-1)}=t_{0.005,4}=4.604$

*Use a t-table.

Construct the 99% confidence interval as follows:

$CI=\bar x\pm t_{\alpha/2, (n-1)}\times \frac{s}{\sqrt{n}}\\=231.134\pm 4.604\times \frac{1.505}{\sqrt{5}}\\=231.134\pm3.099\\=(228.035, 234.233)$

Thus, the 99% confidence interval is (228.035, 234.233).

Answer from: Quest

a) one student is chosen from classroom a, then a student is chosen from classroom b.

step-by-step explanation:

independent events are ones in which the probability of one event does not affect the probability of the second event.

one student is chosen from classroom a; this does not affect the chances of choosing a student from classroom b. this makes these independent events.

when one card is chosen from a standard deck and then set aside before a second card is chosen, the probability of the second card being chosen changes. this makes them dependent events.

when one student is chosen from classroom a and then a second student is chosen from classroom a, the probability of choosing the second student changes. this makes them dependent events.

when a letter is chosen from the alphabet and then a second letter is chosen, the probability of choosing the second letter changes. this makes them dependent events.

Answer from: Quest

Ibelieve the answer is c

Other questions on the subject: Mathematics

Mathematics, 21.06.2019 15:30, 24lfoster

According to statistics a person will devote 32 years to sleeping and watching tv. the number of years sleeping will exceed the number of years watching tv by 18. over a lifetime, how many years will the person spend on each of these activities

Answers: 1

continue

Mathematics, 21.06.2019 18:30, Alexandragurule18

Can someone check if i did this correct. it’s number 4 if you’re wondering.

Answers: 1

continue

Mathematics, 21.06.2019 19:00, aceves5493

After t seconds, a ball tossed in the air from the ground level reaches a height of h feet given by the equation h = 144t-16t^2. after how many seconds will the ball hit the ground before rebounding?

Answers: 2

continue

Mathematics, 21.06.2019 20:00, JOEFRESH10

The table shows the age and finish time of ten runners in a half marathon. identify the outlier in this data set. drag into the table the ordered pair of the outlier and a reason why that point is an outlier.

Answers: 1

continue

You know the right answer?

Ask Your Teacher A journal article reports that a sample of size 5 was used as a basis for calculati...