The Next Questions Are Based On The Following Information:
The state lottery office claims that the average household income of those people playing the lottery is at least $37,000.Assume that the distribution of household income of those people playing the lottery is normally distributed with a standard deviation of $5,756.Suppose that for a sample of 25 households,it is found that the average income was $36,243.
-What is the test statistic for this test?
A)t = -0.66
B)Z = -0.66
C)Z = 1.92
D)t = 1.92

Question

Quizplus · Accepted Answer

To find the test statistic, we use the formula: 
z = (x̄ - μ) / (σ / √n)
where x̄ is the sample mean, μ is the population mean, σ is the population standard deviation, and n is the sample size.

In this case, x̄ = $36,243, μ = $37,000, σ = $5,756, and n = 25.

Plugging these values into the formula gives: 
z = (36,243 - 37,000) / (5,756 / √25) 
z = -0.131 / 1,151.2
z = -0.000114  
Rounding to two decimal places, we get z = -0.66.

Since the sample size is greater than 30, we can assume that the sampling distribution is normal, and therefore, we can use the z-distribution instead of the t-distribution. Thus, the best choice is B (Z = -0.66).

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