Question

Watch Corporation of Switzerland claims that its watches on average will neither gain nor lose time during a week. A sample of 18 watches provided the following gains (+) or losses (–) in seconds per week.

Excel Data File
watches
-0.30
-0.27
-0.34
-0.25
0.31
-0.20
0.36
0.24
-0.19
-0.40
-0.49
-0.55
-0.55
-0.67
-0.03
-0.23
-0.54
0.08

–0.30	–0.27	–0.34	–0.25	+0.31	–0.20	+0.36	+0.24	–0.19
–0.40	–0.49	–0.55	–0.55	–0.67	–0.03	–0.23	–0.54	+0.08

a-1.	Is it reasonable to conclude that the mean gain or loss in time for the watches is 0? Use the .02 significance level. At a level of .02 significance, we reject H0: μ = 0 if t < or t > . (Negative amounts should be indicated by a minus sign. Round your answers to 3 decimal places.)

a-2.	The value of the test statistic is  . (Negative amount should be indicated by a minus sign. Round your answer to 3 decimal places.)

a-3.	(Click to select)  Reject  Do not reject  H0: μ = 0. The p-value is  (Click to select)  greater than 0.20  between 0.0005 and 0.001  less than 0.001  between 0.001 and 0.01

Answer 1

let X be the random variable denoting the gains (+) or losses (–) in seconds per week.

Follow this table for the calculations

	-0.3	0.005878
	-0.27	0.002178
	-0.34	0.013612
	-0.25	0.000711
	0.31	0.284441
	-0.2	0.000544
	0.36	0.340274
	0.24	0.214675
	-0.19	0.001111
	-0.4	0.031212
	-0.49	0.071113
	-0.55	0.106713
	-0.55	0.106713
	-0.67	0.199514
	-0.03	0.037376
	-0.23	4.45E-05
	-0.54	0.10028
	0.08	0.092009
total	-4.02	1.6084
average	-0.22333

We want to test:

The test statistic to test this hypothesis:

Value of test statistic from sample,

P-value = 2*min(P[T>-3.081, T<-3.081])= 2*min(0.997,0.003)=0.06

P-value > 0.02, we fail to reject H_0, since p-value is less than level of significance, hence, we do not evidence to reject the null hypothesis.

P-value is between 0.001 and 0.01