a) The provided sample mean is "\\bar{X}=2770" and the sample standard deviation is "s=554."
The size of the sample is "n=20" and the required confidence level is 95%.
The number of degrees of freedom are "df=20-1=19," and the significance level is "\\alpha=0.05."
Based on the provided information, the critical t-value for "\\alpha=0.05" and "df=19" degrees of freedom is "t_c=2.093."
The 95% confidence for the population mean "\\mu" is computed using the following expression
"=(2770-\\dfrac{2.093\\times 554}{\\sqrt{20}},2770+\\dfrac{2.093\\times 554}{\\sqrt{20}})="
"=(2511, 3029)"
"2511\\leq\\mu\\leq3029"
b) The critical t-value for "\\alpha=0.05" and "df=19" degrees of freedom (left-tailed) is "t_c=-1.729."
"\\mu\\leq2556"
c) The critical t-value for "\\alpha=0.05" and "df=19" degrees of freedom (right-tailed) is "t_c=1.729."
"\\mu\\geq2984"
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