Amanufacturer wants to increase the shelf life of a line of cake mixes. past records indicate that the average shelf life of the mix is 216 days. after a revised mix has been developed, a sample of nine boxes of cake mix gave these shelf lives (in days): 215, 217, 218, 219, 216, 217, 217, 218, and 218. using α = 0.025, has the shelf life of the cake mix increased?

yes, because computed t is less than the critical value.
yes, because computed t is greater than the critical value.
no, because computed t lies in the region of acceptance.
no, because 217.24 is quite close to 216.


using a 5% level of significance and a sample size of 25, what is the critical value for a one tailed hypothesis test?



the mean length of a small counter balance bar is 43 millimeters. there is concern that the settings of the machine producing the bars have changed. test the claim at the 0.02 level that there has been no change in the mean lengh. the alternate hypothesis is that there has been a change. twelve bars (n=12) were selected at random and thier lenghts recorded. the lenghts are (in millimeters) 42, 39, 42, 45, 43, 40, 39, 41, 40, 42, 43 and 42. the mean of the sample is 41.5 and the standard deviation 1.784. has there been a statistically significan change int he mean length of the bars?