Question

In: Statistics and Probability

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

Solutions

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 2 years ago
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