The piston diameter of a certain hand pump is 0.5 inch. the manager determines that the diameters are normally​ distributed, with a mean of 0.5 inch and a standard deviation of 0.004 inch. after recalibrating the production​ machine, the manager randomly selects 29 pistons and determines that the standard deviation is 0.0036 inch. is there significant evidence for the manager to conclude that the standard deviation has decreased at the alpha equals 0.01 level of​ significance?

Solution: The null and alternative hypotheses are:

Under null hypothesis, the test statistic is:

Now, the critical value of at 0.01 level of significance for is:

Since the test statistic, is less than the critical value,, therefore, we fail to reject the null hypothesis and there is not significant evidence for the manager to conclude that the standard deviation has decreased at the alpha equals 0.01

to determine the unit cost your would divide the total cost by the number sold.

7 bagels for $4.41       $4.41/7 = $.63 each at fresh side

5 bagels for $3.60         $3.60/5 = $.72 each at value mart

b because it contains 40% of the possible results from the random list.  

0,1,2,3 v 4,5,6,7,8,9  

4 integers to 6 integers  

40% success vs 60% fail

step-by-step explanation: