The standard error SE SE SE is calculated using the formula:
SE=σn=0.0820≈0.0179 SE = \frac{\sigma}{\sqrt{n}} = \frac{0.08}{\sqrt{20}} \approx 0.0179 SE=nσ=200.08≈0.0179
The test statistic ttest t_{\text{test}} ttest is calculated using the formula:
ttest=xˉ−μ0SE=2.65−2.60.0179≈2.7951 t_{\text{test}} = \frac{\bar{x} - \mu_0}{SE} = \frac{2.65 - 2.6}{0.0179} \approx 2.7951 ttest=SExˉ−μ0=0.01792.65−2.6≈2.7951
For a right-tailed test, the p-value is calculated as:
P=1−T(z)≈0.0058 P = 1 - T(z) \approx 0.0058 P=1−T(z)≈0.0058
Since the sample size is n=20 n = 20 n=20 and the population standard deviation is unknown, we use the t-distribution for this hypothesis test.
The test statistic is t≈2.7951 t \approx 2.7951 t≈2.7951, the p-value is 0.0058 0.0058 0.0058, and the distribution used is the T distribution.
Thus, the answer is:
T distribution (invT for critical value)\boxed{\text{T distribution (invT for critical value)}}T distribution (invT for critical value)
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