Question

The mean work week for engineers in start-up companies is claimed to be about 64 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? proportion mean b. The null hypothesis (or company claim), in symbols, is d = 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 64 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 no 7:50 PM

Answer 1

a) she is testing a mean.

b)

null hypothesis is that the mean is 64 hours.
c) Number of Data Values = 10

x̄ = Sample Mean = 57

standard error = 6/sqrt(10) = 1.897

z = (x-m)/s. =  (57 - 64) / 1.897 =-3.690

the probability is 0.000112

d)

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 64 hours.