Reference no: EM1316997

Q1) From past records it is known that average life of battery used in digital clock is 305 days.  Lives of batteries are normally distributed.  Battery was recently modified to last longer.  A sample of 20 of modified batteries was tested.  It was discovered that mean life was 311 days and sample standard deviation was 12 days.  We desire to test at 0.05 level of significance whether modification increases the life of battery.  What is our decision rule?

a) Don't reject null hypothesis if calculated t is 1.96 or greater

b) Reject null hypothesis if calculated t is less than 1.96

c) Don't reject null hypothesis if calculated t is 1.729 or greater

d) Reject null hypothesis if calculated t is 2.494 or greater

e) None of the above

Q2) Mean length of small counter balance bar is 43 millimetres. There is concern that adjustments of machine producing the bars have changed.  Test claim at 0.02 level that there has been no change in mean length.   Alternate hypothesis is that there has been a change.  12 bars (n = 12) were chosen at random and their lengths recorded.  Lengths are (in millimetres) 42, 39, 42, 45, 43, 40, 39, 41, 40, 42, 43 and 42.  Mean of sample is 41.5 and standard deviation 1.784.  Calculated t = - 2.913.  Has there been a statistically significant change in mean length of the bars?

a) Yes, as the computed t lies in the area beyond the critical.  

b) No, as the information given is not complete.

c) No, as the computed t lies in the area to the right of -2.913.

d) None of the above