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=0.01​, test the claim that the mean salary is ​$97,000.   Complete parts​ (a) through​ (e) below. Assume the population is normally distributed. Annual Salaries: 100,581 96,242 93,539 112,657 82,569 74,152 76,950 80,943 102,375 76,134 103,984 104,077 91,100 82,131 85,136 110,416     ​(a) Identify the claim and state H0 and Ha. H0: Ha:   ​(Type integers or decimals. Do not​ round.)     The claim is the________hypothesis

Definition Definition Measure of central tendency that is the average of a given data set. The mean value is evaluated as the quotient of the sum of all observations by the sample size. The mean, in contrast to a median, is affected by extreme values. Very large or very small values can distract the mean from the center of the data. Arithmetic mean: The most common type of mean is the arithmetic mean. It is evaluated using the formula: μ = 1 N ∑ i = 1 N x i Other types of means are the geometric mean, logarithmic mean, and harmonic mean. Geometric mean: The nth root of the product of n observations from a data set is defined as the geometric mean of the set: G = x 1 x 2 ... x n n Logarithmic mean: The difference of the natural logarithms of the two numbers, divided by the difference between the numbers is the logarithmic mean of the two numbers. The logarithmic mean is used particularly in heat transfer and mass transfer. ln x 2 − ln x 1 x 2 − x 1 Harmonic mean: The inverse of the arithmetic mean of the inverses of all the numbers in a data set is the harmonic mean of the data. 1 1 x 1 + 1 x 2 + ...