A hypothesis will be used to test that a population mean equ

A hypothesis will be used to test that a population mean equals 7 against the alternative that the population mean docs not equal 7 with known variance sigma. What are the critical values for the test statistic Z0 for the following significance levels? 0.01 0.05 0.10 5. A hypothesis will be used to test that a population mean equals 5 against the alternative that the population mean is less than 5 with known variance sigma. What is the critical value for the test statistic Z0 for the following significance levels? 0.01 0.05 0.10 The mean water temperature downstream from a power plant cooling tower discharge pipe should be no more than 100degreeF. Past experience has indicated that the standard deviation of temperature is 2degreeF. The water temperature is measured on nine randomly chosen days, and the average temperature is found to be 98degreeF. Is there evidence that the water temperature is acceptable at alpha = 0.05? What is the P-value for this test? A bearing used in an automotive application is supposed to have a nominal inside diameter of 1.5 inches. A random sample of 25 bearings is selected and the average inside diameter of these bearings is 1.4975 inches. Bearing diameter is known to be normally distributed with standard deviation alpha inch.

Solution

a) 0.01 (-2.58<z<2.58)

b_ 0.05 (-1.96<z<1.96)

c) 0.10 (-1.64<z<1.64)

5) 0.01 Z<2.33

0.05 z<1.645

0.10 Z< 1.28

6) z = 98-100/(2/3) = -3

p value = 0.00135

Reject null hypothesis.

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7) z value = (1.4975-1.5)/0.01/5 = -1.25

p valu e=0.2113

Accept null hypothesis.