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Homework answers / question archive / 1)A researcher is testing a hypothesis of a single mean
1)A researcher is testing a hypothesis of a single mean. The critical z value for α = .05 and an critical value for a one tailed right test is 1.645. The observed (test statistic) z value from sample data is 1.13. The decision made by the researcher based on this information is to _________ the null hypothesis.
2)Elwin Osbourne, CIO at GFS, Inc., suspects that at least 25% of e-mail messages sent by GFS employees are not business related. A random sample of 300 e-mail messages was selected to test this hypothesis at the 0.01 level of significance. Fifty-four of the messages were not business related. The appropriate decision is
Answer:
1) The decision made by the researcher based on this information is to ACCEPT the null hypothesis.
2)
Observed proportion = 54 / 300 = 0.18
Hypothesized proportion = 0.25
S.Error = sqrt ( 0.25 * 0.75 / 300)
= 0.025
Thus,
Z- value = 0.18 - 0.25 / 0.025
= -2.8
Thus, the proportions are different since Z-critical = -2.58
Null hypothesis is rejected.
