Question

Previously, 5​% of mothers smoked more than 21 cigarettes during their pregnancy. An obstetrician believes that the percentage of mothers who smoke 21 cigarettes or more is less than 5​% today. She randomly selects 145 pregnant mothers and finds that 4 of them smoked 21 or more cigarettes during pregnancy. Test the​ researcher's statement at the α=0.05 level of significance.

What are the null and alternative​ hypotheses?

H0​:p =0.05 versus H1​: p <0.05

​(Type integers or decimals. Do not​ round.)

Because np0(1 - p0)=____ < ​10, the normal model (may/may not) be used to approximate the​ P-value.

​(Round to one decimal place as​ needed.)

Find the​ P-value.

​P-value=____

​(Round to three decimal places as​ needed.)

Is there sufficient evidence to support the​ obstetrician's statement?

A. No​, do not reject the null hypothesis because the​ P-value is greater than α. There is not sufficient evidence to conclude that the percentage of mothers who smoke 21 or more cigarettes during pregnancy is less than 5​%.

B. Yes​, reject the null hypothesis because the​ P-value is less than α. There is sufficient evidence to conclude that the percentage of mothers who smoke 21 or more cigarettes during pregnancy is less than 5​%.

C. Yes​, do not reject the null hypothesis because the​ P-value is greater than α. There is sufficient evidence to conclude that the percentage of mothers who smoke 21 or more cigarettes during pregnancy is less than 5​%.

D. No​, reject the null hypothesis because the​ P-value is less than α. There is not sufficient evidence to conclude that the percentage of mothers who smoke 21 or more cigarettes during pregnancy is less than 5​%.

Answer 1

The statistical software output for this problem is:

Hence,

Because np0(1 - p0)= 6.9 < ​10, the normal model may not be used to approximate the​ P-value.

P-value = 0.108

No​, do not reject the null hypothesis because the​ P-value is greater than α. There is not sufficient evidence to conclude that the percentage of mothers who smoke 21 or more cigarettes during pregnancy is less than 5​%.

Option A is correct.