Question 1120080: #15
The mean work week for engineers in start-up companies is claimed to be about 65 hours with a standard deviation of 6 hours. Kara, a newly hired engineer hopes that it's not (she wants it to be shorter). She asks 10 engineers in start-ups for the lengths of their mean work weeks. Their responses are 70,45,55,60,65,55,55,60,50,55.
a. Is the newly hired engineer testing a mean or a proportion?
mean or proportion
b. The null hypothesis (or company claim), in symbols, is μ=.
c. If the claim is correct, what is the probability that a sample mean would be as low as Kara's mean?
_____% (Give your answer as a percentage accurate to one decimal place.)
d. If Kara will accept the 65 hours as the real average so long as there's at least a 10% chance the sample average value could be as low as hers, should she accept the claim?
yes or no
Answer by Theo(13342)   (Show Source):
You can put this solution on YOUR website! population mean is reported as 65 hours with a standard deviation of 6 hours.
sample size is 10.
mean of sample is equal to 57.
standard error = population standard deviation divided by square root of sample size equals 6/sqrt(10) = 1.897366596
z = (x-m)/s.
z equals z-score
x equals raw score
m equals raw mean
s equals standard error.
z = (x-m)/s becomes z = (57 - 65) / 1.897366596 which becomes z = -4.216370215.
the probability of getting a z-score of -4.216370215 in a sample of size 10 is equal to .0000124212457.
this is an extraordinarily low probability which means the likelihood of getting a sample of size 10 with a mean of 57 is overwhelmingly not due to random variations in the mean of samples of size 10.
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The mean work week for engineers in start-up companies is claimed to be about 65 hours with a standard deviation of 6 hours. Kara, a newly hired engineer hopes that it's not (she wants it to be shorter). She asks 10 engineers in start-ups for the lengths of their mean work weeks. Their responses are 70; 45; 55; 60; 65; 55; 55; 60; 50; 55.
a. Is the newly hired engineer testing a mean or a proportion?
she is testing a mean.
b. The null hypothesis (or company claim), in symbols, is μ=65.
null hypothesis is that the mean is 65 hours.
c. If the claim is correct, what is the probability that a sample mean would be as low as Kara's mean (give your answer as a percentage accurate to one decimal place)?
the probability would be .0000124212457.
d. If Kara will accept the 65 hours as the real average so long as there's at least a 10% chance the sample average value could be as low as hers, should she accept the claim?
she should not accept the claim.
the probability that the average of her sample of size 10 being 57 is due to random variations in the mean of any sample taken is remote.
it more than likely indicates that the real average is less than 65 hours.
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