Question

Consider the hypotheses shown below. Given that x over bar (x) equals 112​, sigma (standard deviation) equals 26​, n equals 40​, alpha (a) equals 0.05​, complete parts a and b. Upper H 0​: mu equals 118 Upper H 1​: mu not equals 118

a. What conclusion should be​ drawn?

b. Determine the​ p-value for this test.

what is the critical z-score? and can someone please show me how to find the critical z- score please

Answer 1

a) Sample size = n = 40

Sample mean = = 112

Population standard deviation = = 26

The null and alternative hypothesis is

Level of significance = 0.05

Here population standard deviation is known so we have to use z-test statistic.

Test statistic is

Critical value = 1.96    ( Using z table)

Critical value > Test statistic | z | we fail reject the null hypothesis.

Conclusion: The population mean is 118.

b)

P-value = 2*P(Z < - 1.46) = 2*0.0722 = 0.1444

( From z table)

Lets show how to find the critical value.

By using z table we can easily find the critical value.

Level of significance = = 0.05

1 - = 1 - 0.05/2 = 0.9750

Search the value 0.9750 in the body of the table and corresponding row and column.

We will get critical z-score = 1.96

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