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Answer:
The test statistic is -0.19.
Step-by-step explanation:
We are given that in 1973, the GSS included questions about the number of hours that the respondent worked per week. A sample of 30 respondents was questioned. The average number of hours worked per week was 39.49 hours with a standard deviation of 14.86 hours.
We have to test the hypothesis that did Americans work less than 40 hours a week on average in 1973 or not.
Let Null Hypothesis, [tex]H_0[/tex] : [tex]\mu[/tex] [tex]\geq[/tex] 40 hours {means that Americans work greater than or equal to 40 hours a week on average in 1973}
Alternate Hypothesis, [tex]H_a[/tex] : [tex]\mu[/tex] < 40 hours {means that Americans work less than 40 hours a week on average in 1973}
The test statistics that will be used here is One-sample t-test ;
T.S. = [tex]\frac{\bar X - \mu}{\frac{s}{\sqrt{n} } }[/tex] ~ [tex]t_n_-_1[/tex]
where, [tex]\bar X[/tex] = sample average number of hours worked per week = 39.49
[tex]s[/tex] = sample standard deviation = 14.86 hours
n = sample of respondents = 30
[tex]\mu[/tex] = population mean
SO, test statistics = [tex]\frac{39.49-40}{\frac{14.86}{\sqrt{30} } }[/tex] ~ [tex]t_2_9[/tex]
= -0.19
Therefore, the value of test statistic is -0.19.
The test statistic of the given hypothesis is; C: -0.19
What is the test statistic?
We want to find whether Americans work less than 40 hours. Let us first define the hypothesis;
Null Hypothesis; H₀: μ ≥ 40
Alternative Hypothesis; μ < 40
We are given;
Sample mean; x' = 39.49
Standard deviation; σ = 14.86
Formula for test statistic is;
z = (x' - μ)/σ
z = (39.49 - 40)/14.86
z = -0.19
Read more about Test Statistics at; https://brainly.com/question/15980493
