Question

Lisa, a dentist, believes not enough teenagers floss daily. She would like to test the claim that the proportion of teenagers who floss twice a day is less than 40%. To test this claim, a group of 400 teenagers are randomly selected and its determined that 149 floss twice a day. The following is the setup for this hypothesis test: H0:p=0.40 H0:p<0.40 The p-value for this hypothesis test is 0.131. At the 5% significance level, should the dentist reject or fail to reject the null hypothesis?

Answer 1

The dentist should fail to reject the Null hypothesis

Explanation:

From the question we are told that

The sample size is n = 400

The sample mean is
`\= x = 149`

The level of significance is 5% = 0.05

The Null hypothesis is
`H_o : p = 0.40`

The Alternative hypothesis is
`H_a : p < 0.40`

The p-value is
`p-value = 0.131`

Looking at the given data we can see that the p-value is greater than the level of significance hence the dentist should fail to reject the Null hypothesis