Consider the following sample observations: 2781, 2900, 3013, 2856, and 2888 upp

Question

Consider the following sample observations: 2781, 2900, 3013, 2856, and 2888 uppose-we-want to test-whether there is evidence that mu-3000 a) Write the appropriate hypotheses, compute the p-value, and state the conclusion. "In English'.'ti.e.. , ts there evidence that-ma is, ress-than-3000?) using alpha = 0.05 Compute the appropriate confidence intervat:tcr)Is the conclusion the sa as in part a? Explain. me One can also arrive at the same conclusion, without the P-value and cI, by what jas-called the-rejection method. I'll-war-you through-ttt c) If HO is true, compute the value of x bar that has an area of aipha-0.05 to he left. This value of x bar is called the critical valver and the region its left is called the rejection region. So, in this part of the problem you are computing the reject d) Is the observed value of x bar in the rejection region? If so, one can reject H0 in favor of Hi: otherwise, one cannot sey anything

Explanation / Answer

p-value

One-Sample T: C2

Test of = 3000 vs < 3000

Variable N    Mean StDev SE Mean 95% Upper Bound      T      P
C2        5 2887.6   84.0     37.6           2967.7 -2.99 0.020

p-value = 0.02 < 0.05

we reject the null hypothesis

Note that p-value in left-tailed test is P(t < -2.99) = 0.02   {not P(T > -2.99)   as Ha: mu < 3000}

confidence interval

95% confidence interval

(2783.3, 2991.9)

since each value is less than 3000 ,

we reject the null ,

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