An employment information service claims the mean annual salary for senior level product engineers is ​$97,000. The annual salaries​ (in dollars) for a random sample of 16 senior level product engineers are shown in the table to the right. At α=0.10​, test the claim that the mean salary is ​$97,000. Complete parts​ (a) through​ (e) below. Assume the population is normally distributed.        Annual Salaries  100 ​,637 96 ​,395 93 ​,509 112 ​,609   82 ​,472 74 ​,162 76 ​,989 80 ​,977 102 ​,467 76 ​,251 103 ​,944 104 ​,042 91 ​,135 82 ​,152 85 ​,096 110 ​,269     Part 1 ​(a) Identify the claim and state H0 and Ha.     ​(Type integers or decimals.) Part 2 ​(b) Use technology to find the critical​ value(s) and identify the rejection​ region(s).   The critical​ value(s) is/are t0= ​ ​(c) Find the standardized test​ statistic, t.   The standardized test statistic is t=   Part 5 ​(d) Decide whether to reject or fail to reject the null hypothesis.     Part 6 ​(e) Interpret the decision in the context of the original claim.   There (is not/is) enough evidence at the ___% level of significance to (reject /support) the claim that the mean annual salary for senior-level product engineers is equal to $_______

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An employment information service claims the mean annual salary for senior level product engineers is ​$97,000. The annual salaries​ (in dollars) for a random sample of 16 senior level product engineers are shown in the table to the right. At α=0.10​, test the claim that the mean salary is ​$97,000.

Complete parts​ (a) through​ (e) below. Assume the population is normally distributed.

 
 
 
 Annual Salaries 
100
​,637
96
​,395
93
​,509
112
​,609
 
82
​,472
74
​,162
76
​,989
80
​,977
102
​,467
76
​,251
103
​,944
104
​,042
91
​,135
82
​,152
85
​,096
110
​,269
 
 
Part 1
​(a) Identify the claim and state
H0
and
Ha.
 
 
​(Type integers or decimals.)
Part 2
​(b) Use technology to find the critical​ value(s) and identify the rejection​ region(s).
 
The critical​ value(s) is/are t0=
​(c) Find the standardized test​ statistic, t.
 
The standardized test statistic is t=
 
Part 5
​(d) Decide whether to reject or fail to reject the null hypothesis.
 
 
Part 6
​(e) Interpret the decision in the context of the original claim.
 
There (is not/is) enough evidence at the ___% level of significance to (reject /support) the claim that the mean annual salary for senior-level product engineers is equal to $_______

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