Question

I have trouble when solving this problem. I don't understand "There are more than half of the Final scores " could refer to which? Please help me in solving this.

Test the hypothesis that there are more than half of the Final scores that are 5 or below, at the significance level of 5%.

Final Scores

9.2 4.8 6.6 5.8 3.4 5 5.8 3.4 2.2

Answer 1

Population proportion: P = 0.50,

Sample size: n= 9,

here 5 number are less than 5 in the given sample.

Numbers in sample less than five : x= 5,  

= 5% = 0.05

The null and alternative hypothesis is

Ho: P   0.5

H1: P > 0.5

formula for test statistics is

z = 0.3333

test statistics: z = 0.33

calculate P-Value

P-Value = 1 - P(z < 0.33 )

using z table we get

P(z < 0.33 ) = 0.6293

P-Value = 1 - 0.6293

P-Value = 0.3707

decision rule is

Reject Ho if ( P-value ) ( )

here, ( P-value= 0.3707 ) > ( = 0.05 )

Hence, we can say,

Do not reject null hypothesis.

Therefore there is not  enough evidence to support the claim that more than half of the Final scores that are 5 or below, at the significance level of 5%.