Question

Taylor reads that 65% of men do not wassh their hands after going to the resteroom. He camps put in a restroom and randomly observes 40 men. Of these 40 men, 30 do not wash their hands. Is this a significantly different percentage at the 1% level of significance?

Answer 1

n = sample size = 40

x = men who do not washes their hands = 30

We write the hypotheis as

Different percentage means the percetage is not equal to

We use the test statistics formula

Where

p = 0.65   given percentage as 65% so we convert that into decimal .

n = 40

Test statistics =

Our test is two tailed test beacuse it contain not equal to sign in the alternative hypothesis (H_a)

Now we find the crtical value

This test has two critical with opposite sign because the test is 2 tailed

Now use the Excel command to find the critical value

Select empty cell from excel and type

Do not forget to type = sign

=NORMSINV(0.005)

Left side Critical value =- 2.575829304

Now for the right side critcal value

Area = 1 - 0.005 = 0.995

Use the excel command

Select empty cell and type

=NORMSINV(0.995)

Do not forget to type = sign

Right side critical value = 2.575829304

Decision rule

1 ) If the test statistics lies between two critcal value then we   Fail to reject H₀

2 ) Othere we We reject H₀

Our test statistics value = 1.325987088

Now look 1.325987088 lies in between -2.575829304   and 2.575829304

i.e -2.575829304 <   1.325987088 < 2.575829304

Therefore the decision is

We Fail to reject H₀ ( Null hypothesis is not rejected )

Is this a significantly different percentage at the 1% level of significance?

Answer : NO ( here we are Not rejecting H₀)