Calculate the test statistic and p-value for each sample. Use Appendix C-2 to ca

Question

Calculate the test statistic and p-value for each sample. Use Appendix C-2 to calculate the p-value. (Negative values should be indicated by a minus sign. Round your test statistic to 3 decimal places and p-value to 4 decimal places.)

Test Statistic and p-value

(a) H0: formula62.mml 0.50 versus H1: formula62.mml > 0.50, = 0.05, x = 51, n = 82

(b) H0: formula62.mml = 0.30 versus H1: formula62.mml 0.30, = 0.05, x = 15, n = 41

(c) H0: formula62.mml 0.10 versus H1: formula62.mml < 0.10, = 0.01, x = 4, n = 104

Explanation / Answer

(a) H0: formula62.mml 0.50 versus H1: formula62.mml > 0.50, = 0.05, x = 51, n = 82

p= x/n= 51/82= 0.62

P=0.5

Q=1-0.5= 0.5

Under null hypothesis test statistic is

Z= 0.62-0.5/sqrt(PQ/n)

Z= 0.12/sqrt(0.003)

Z= 0.12/0.055

Z=2.18

Z critical value = 1.645 for right tailed test.

SInce critical value is smaller than calclated value, we reject null hypothesis.

The P-Value is 0.014629.The result is significant at p < 0.05.

b) H0: formula62.mml = 0.30 versus H1: formula62.mml 0.30, = 0.05, x = 15, n = 41

p= x/n= 15/41= 0.37

P= 0.3

Q=1-P= 1-0.3= 0.7

Z= 0.37-0.3/sqrt(PQ/n)

= 0.07/sqrt(0.005)

= 0.07/0.071

Z=0.98

The P-Value is 0.3271. The result is not significant at p < 0.05. Fail to reject NULL HYPOTHESIS H0

c)  H0: formula62.mml 0.10 versus H1: formula62.mml < 0.10, = 0.01, x = 4, n = 104

p= 4/104= 0.038

P= 0.1

Q=1-P= 1-0.1= 0.9

Z= 0.038-0.1/SQRT(0.1*0.9/104)

= -0.062/0.029

Z= -2.14

The P-Value is 0.0162.The result is not significant at p < 0.01. Fail to reject null hypothesis H0

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