Question

You would like to determine if more than 50% of the observations in a population are below 10. At α= 005, conduct the test on the basis of the following 20 sample observations: (You may find it useful to reference the appropriate table: z table or t table) 12 14 12 6 11 4 13 10 a. Select the null and the alternative hypotheses. HO: p = 0.50; HA: p # 0.50 0H0 : p 0.50; HA : p > 0.50 Ho: p2 0.50; HA: p<.50 b. Calculate the sample proportion. (Round answer to 2 decimal places.) Sample proportion c. Calculate the value of test statistic. (Round answer to 2 decimal places.) Test statistic

Answer 1

a)  

b) Sample Proportion is

$\widehat{p} =\frac{X}{n} =\frac{13}{20}= 0.65$

c) The test statistic is

$Z =\frac{\widehat{p}-p}{\sqrt{pq/n}} = \frac{0.65-0.5}{\sqrt{0.25/20}}=1.34$

The critical value of Z is 1.645

Since Z calculated is less than Z tabulated.Fail to Reject H0