A pharmaceutical company develops a drug that the claim reduces the percentage of kids that are...

A pharmaceutical company develops a drug that the claim reduces the percentage of kids that are allergic to tree nuts . Suppose it is believed that 14% of kids are allergic to tree nuts. In a recent the company says that only 9% of kids that took the medication were allergic to tree nuts. The pharmaceutical company claims that that this drug has reduced the percentage of kids allergic to tree nuts. In a hypothesis test to test this claim we get the following null and alternative hypotheses.

H0:p=0.14H0:p=0.14
H1:p<0.14H1:p<0.14

If the conclusion is to fail to reject the null hypothesis, what is the conclusion in regards to the original claim?

There is not sufficient sample evidence to warrant rejection of the claim that the new drug has reduced the percentage of kids allergic to tree nuts
There is sufficient sample evidence to warrant rejection of the claim that the new drug has reduced the percentage of kids allergic to tree nuts
There is not sufficient sample evidence to support the claim that the new drug has reduced the percentage of kids allergic to tree nuts
There is sufficient sample evidence to support the claim that the new drug has reduced the percentage of kids allergic to tree nuts

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Expert Solution

Statistics and Probability

A pharmaceutical company develops a drug that the claim reduces the percentage of kids that are allergic to tree nuts . Suppose it is believed that 14% of kids are allergic to tree nuts. In a recent the company says that only 9% of kids that took the medication were allergic to tree nuts. The pharmaceutical company claims that that this drug has reduced the percentage of kids allergic to tree nuts. In a hypothesis test to test this claim we get the following null and alternative hypotheses.

H0:p=0.14
H1:p<0.14
using excel>addin>phstat>one sample test

we have

Z Test of Hypothesis for the Proportion

Data
Null Hypothesis p =	0.14
Level of Significance	0.05
Number of Items of Interest	9
Sample Size	100

Intermediate Calculations
Sample Proportion	0.09
Standard Error	0.0347
Z Test Statistic	-1.4410

Lower-Tail Test
Lower Critical Value	-1.6449
*p-Value*	0.0748
Do not reject the null hypothesis

since p value is more than 0.05 so do not reject Ho

There is not sufficient sample evidence to support the claim that the new drug has reduced the percentage of kids allergic to tree nuts

orchestra answered 1 year ago

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