Question

A random sample of n=75 is taken from a population of values to test the statistical hypotheses H0:μ=99HA:μ≠99 The mean, median, and standard deviation of this sample were found to be: X¯¯¯¯=100.01X˜=101.12S=8.61 (a) Find the value of the test statistic, using at least three decimals in your answer. Note: Minitab may only give you two digits, if that is the case then calculate by hand. test statistic = (b) The P-value was found to be 0.3129398, or 31.29398%. Select the probability expression that was used to find the P-value. A. P(ZTcalc) C. P(Z≠Zcalc) D. P(T74>Tcalc)∗2 E. P(Z>Zcalc)∗2 F. P(T74≠Tcalc) G. P(T74

Answer 1

Solution :

This is the two tailed test .

The null and alternative hypothesis is ,

H₀ :   = 99

H_a :    99

= 100.01

= 99

S = 8.61

n = 75

df = n - 1 = 75 - 1 = 74

Test statistic = t

= ( - ) / S / n

= (100.01 - 99) / 8.61 / 75

= 1.0159

Test statistic = 1.0159

P-value = 0.313

P(T74 ≠ Tcalculated)