2. Formulating hypotheses and determining whether a test is one-or two-tailed

To identify the correct Z(critical), it is important to determine whether the hypothesis test is one-tailed or two-tailed. The decision between a one- and two-tailed hypothesis is based on the researcher's expectations about the population from which the sample was selected.

An electricians' union is widely known for the extremely high quality of their installations. You hypothesize that unionized electricians have shorter work days. Assume that the the average number of hours of a work day is 8.3 hours. You obtain a sample that yields a sample mean of X

= 7.7 hours.

Let denote the average number of hours of a work day. Formulate your null and research hypotheses by selecting the appropriate values in the dropdown menus that follow.

H0

:
(H1

:

)

The test you conduct is test.

Note: A one-tailed test is described as a lower-tailedtest if the null hypothesis is rejected for values of the test statistic in the lower tail of its distribution, and it is described as an upper-tailedtest if the null hypothesis is rejected for values of the test statistic in the upper tail of its distribution.

Use the distribution tables to complete the exercises that follow.

0.0000 Area Beyond Z 0.0013

0.0014 Area Beyond Z 0.0062

0.0064 Area Beyond Z 0.0228

0.0233 Area Beyond Z 0.0668

0.0681 Area Beyond Z 0.1587

0.1611 Area Beyond Z 0.3085

0.3121 Area Beyond Z 0.5000

(a)	(b)	(c)		(a)	(b)	(c)
Z	Area Between Mean and Z	Area Beyond Z		Z	Area Between Mean and Z	Area Beyond Z
0.00	.0000	.5000		0.25	.0987	.4013
0.01	.0040	.4960		0.26	.1026	.3974
0.02	.0080	.4920		0.27	.1064	.3936
0.03	.0120	.4880		0.28	.1103	.3897
0.04	.0160	.4840		0.29	.1141	.3859
0.05	.0199	.4801		0.30	.1179	.3821
0.06	.0239	.4761		0.31	.1217	.3783
0.07	.0279	.4721		0.32	.1255	.3745
0.08	.0319	.4681		0.33	.1293	.3707
0.09	.0359	.4641		0.34	.1331	.3669
0.10	.0398	.4602		0.35	.1368	.3632
0.11	.0438	.4562		0.36	.1406	.3594
0.12	.0478	.4522		0.37	.1443	.3557
0.13	.0517	.4483		0.38	.1480	.3520
0.14	.0557	.4443		0.39	.1517	.3483
0.15	.0596	.4404		0.40	.1554	.3446
0.16	.0636	.4364		0.41	.1591	.3409
0.17	.0675	.4325		0.42	.1628	.3372
0.18	.0714	.4286		0.43	.1664	.3336
0.19	.0753	.4247		0.44	.1700	.3300
0.20	.0793	.4207		0.45	.1736	.3264
0.21	.0832	.4168		0.46	.1772	.3228
0.22	.0871	.4129		0.47	.1808	.3192
0.23	.0910	.4090		0.48	.1844	.3156
0.24	.0948	.4052		0.49	.1879	.3121

Using the significance level of p = 0.01, the critical value(s) for a test of the previously stated null hypothesis is/are .