2. The null hypothesis, H o : = 43, was tested against the alternative hypothesi

Question

2. The null hypothesis, Ho: = 43, was tested against the alternative hypothesis, Ha: > 43. A sample of 74 resulted in a calculated p-value of 0.062. If = 3.1, find the value of the sample mean, x. (Give your answer correct to one decimal place.)

3. The null hypothesis, Ho: = 15.5, was tested against the alternative hypothesis, Ha: < 15.5. A sample of 51 resulted in a calculated p-value of 0.013. If x = 14.5, find the value of the population standard deviation. (Give your answer correct to two decimal places.)

Explanation / Answer

Question 1)

The given hypothesis statement says this is a two-tailed test.

The value of standard deviation is given so we use z-test for single mean.

p-value = 2 * P (Z > z)

z = (x bar - µ) / (s/Ön)

= (1.624-1.587)/(0.26/sqrt(29))

= 0.77

p-value = 2 * P (Z>0.77)

               = 2 *( 1 – P (z<0.77))

               = 2 * ( 1 - 0.7794)

               = 2 *0.2206

               = 0.4412

Answer: 0.4412

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