Question 1157881: An employment information service claims the mean annual salary for senior level product engineers is $99,000. The annual salaries (in dollars) for a random sample of 16 senior level product engineers are shown in the table to the right. At alphaequals0.05, test the claim that the mean salary is $99,000. Complete parts (a) through (e) below. Assume the population is normally distributed
100,568
96,388
93,498
112,763
82,529
74,180
76,994
81,043
102,444
76,222
104,001
103,983
91,064
82,156
85,026
110,338
Answer by Boreal(15235)   (Show Source):
You can put this solution on YOUR website! Use a calculator to get the mean and sd of these data.
The calculator with the t-test (random sample, normal, using sd of sample to approximate sd of distribution).
the mean is $91979.93
sd is $13105.58
the test statistic is t(0.975, df=15)
critical value is |t|>2.131
the calculation is t(0.975,df=15)=(x bar-mean)/s/sqrt(n)
=-7020.07*sqrt(15)/13105.58
= -2.07
The null hypothesis is not rejected at the 0.05 level. There is not sufficient evidence to conclude the true mean is not $99000.
p-value is 0.057
This can be put into the t-test in STAT TESTS, with Data and the same results will be given.
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