SOLUTION: To test the hypothesis H₀:μ=100 against H₁:μ>100, a statistics practitioner randomly sampled 100 observations and found the sample mean =106 and the sample standard deviation

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Question 1183216: To test the hypothesis H₀:μ=100 against H₁:μ>100, a statistics practitioner randomly sampled 100 observations and found the sample mean =106 and the sample standard deviation S=35. Assume a significance level of 1%. Calculate the test statistic
Answer by robertb(5830) About Me  (Show Source):
You can put this solution on YOUR website!
H%5B0%5D%3A++mu+=+100
H%5B1%5D%3A++mu+%3E+100
The statistic to use is t+=+%28%28X-bar%29+-+mu%29%2F%28s%2Fsqrt%28n%29%29, with degree of freedom n-1+=+100+-+1+=+99.
==> t+=+%28106+-+100%29%2F%2835%2Fsqrt%28100%29+%29+=+1.7143, to 4 d.p.
==> P%28t+%3E+1.7143%29+=+0.0448. This is also the p-value for the test.
Since p-value = 0.0448 > 0.01 (the significance level), we don't reject the null hypothesis, and conclude that the population mean is still 100.
(Probabilities were obtained from https://stattrek.com/online-calculator/t-distribution.aspx)