Question

a)  A manager of AAA Supermarket proposed a new strategy to increase sales of products. He believes that the true mean of sales is more than RM2000. Thus, the hypothesis statement is as follow:

H₀: μ > RM2000.

H₁: μ < RM2000.

i.      Comment on the hypothesis statement. Give a correct suggestion.

ii.    What is the other TWO (2) information needed in performing the hypothesis testing in part (b)?

b)    The Health Magazine reported that 17% of children in Bandar A do not eat vegetables. To test this reported value, a researcher surveyed 90 children in Bandar A and found that 22 do not eat the vegetables. There are 2 part.. ((difference method in bi , bii))

i.      Construct 95% confidence interval for the percentage of children who do not eat the vegetables.

ii.    At 5% significance level, test whether the reported value is correct or not.

Answer 1

part a.

Hypothesis statement :

He believes that the true mean of sales is more than RM2000.

When claim has < or > or not equal statment we always write that statement under alternative hypothesis H1.

H0 holds opposite sign of H1. H0 holds always equality statement which is = or .

ii }

For hypothesis testing we need sample data or sample size , standard deviation sample mean all numberical data which need to plug test statsitics. Here they do provide any information for testing.

Part b.

p= 17%= 0.17

x = 22

n = 90

i . Construct confidene interval 95%.

Confidence level = 95% = 0.95

Using Z table for 95% interval Z value is ,

Z = 1.96         ( You can use Excel cammnd as well a = 1-0.95 = 0.05 area = 1-(0.05/2) = 0.975

                                         =NORMSINV(0.975) )

Confidence interval formula :

( 0.1556 , 0. 3332 )

95% confidence interval for the percentage of children who do not eat the vegetables is ( 0.1556 , 0. 3332 )

ii. At 5% significance level, test whether the reported value is correct or not

p =0.17 which lies in interval ( 0.1556 , 0. 3332 ) therefore reported value 17% is not significant (we fails to reject H0 )at 5% significance level. So reported value is correct.