chap10A

# 833 and the10criticalvalueis t c 1383

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Unformatted text preview: ial investment is 10%. Test the company’s claim. How should a hypothesis test be stated ? If there is strong evidence that the mean return on the investment is below 10% this will give a cautionary warning to a potential investor. Therefore, test the null hypothesis: H0 : μ = 10 against the alternative hypothesis: H1 : μ < 10 From a sample of n = 10 observations, the sample statistics are: x = 8.82 and s = 2.40 The t‐test statistic is: 16 t= x − a 8.82 − 10 = = − 1.554 s 2.40 10 n Chapter 10 The calculation of the p‐value for the test is shown in the graph. f(t) PDF of t ( 9 ) area = p-value t = -1.554 0 t Because of symmetry about zero, the p‐value will be identical to the upper tail area, of the probability density function for the t‐distribution with (n–1) = 9 degrees of freedom, to the right of the value of 1.554. With Microsoft Excel the probability is calculated with the function: TDIST( 1.554 , 9, 1) This returns the answer: p‐value = 0.077. 17 Chapter 10 With a sig...
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