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Phoenix [80]
3 years ago
7

A soft-drink machine is regulated so that the amount of drink dispensed is approximately normally distributed with known standar

d deviation, sigma. Given a random sample of n drinks and the sample mean, x-bar, you find a 90% confidence interval for the mean of all drinks dispensed by this machine. Then you calculate a 90% confidence interval (same confidence level) using a larger sample, for example (n 20) drinks. Also, you notice that the sample mean, x-bar, is the same for both samples.
Required:
Was this a reasonable decision?
Mathematics
1 answer:
Vsevolod [243]3 years ago
7 0

Answer:

This is  a reasonable decision because the sample size has no effect on the 90% confidence interval

Step-by-step explanation:

90% confidence interval

larger sample size = 20

condition : sample mean ( x-bar ) is the same for both samples

<em>This is  a reasonable decision because the sample size has no effect on the 90% confidence interva</em>l

<u>from condition 1 :</u>

Amount of drink dispensed is normally distributed with known standard deviation , given a random sample of n drinks and the sample mean at a confidence interval of 90%

<u>for condition 2 :</u>

sample size = 20

mean = 2.25 ( assumed value )

std = 0.15 ( assumed value )

Z = 1.645 ( Z-value )

determine the 90% confidence interval

= mean ± z \frac{std}{\sqrt{n} }

= 2.25 ± 1.645 \frac{0.15}{\sqrt{20} }

= 2.25 ± 0.0335 = ( 2.2835 , 2.2165 )

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