According to Emergency Room Statistics, in any 6 month period, 15.2% of asthmatic children not on inhalers will have an asthmatic complication requiring the emergency room. A pharmaceutical firm has developed a new steroidal inhaler. The company believes that the use of this steroidal inhaler will decrease the percentage of asthmatic children requiring emergency room care for asthmatic complications. Because the FDA requires 2-sided hypothesis tests, the company tested the following claim: In any 6 month period, the percentage of asthmatic children using their steroidal inhaler that require emergency room care for asthmatic complications will not be 15.2%. To test their claim, they took a SRS of 260 asthmatic children and had them use a steroidal inhaler for 6 months. Of the 260 children, 60 required emergency room care for asthmatic complications at some time in the 6 month period. Calculate the test statistic.

Let p be the population proportion of the asthmatic children requires emergency room care for asthmatic complications at some time in the 6 month period.

As per give , we have

[tex]H_0:p=0.152\\\\ H_a: p\neq 0.152[/tex]

Since alternative hypothesis is two-tailed , so test is a two-tailed test.

To test their claim, researcher took a SRS of 260 asthmatic children and had them use a steroidal inhaler for 6 months. Of the 260 children, 60 required emergency room care for asthmatic complications at some time in the 6 month period.

Sample size : n= 260

Sample proportion : [tex]\hat{p}=\dfrac{60}{260}\approx0.231[/tex]

Test statistic : [tex]z=\dfrac{\hat{p}-p}{\sqrt{\dfrac{p(1-p)}{n}}}[/tex]

[tex]z=\dfrac{0.231-0.152}{\sqrt{\dfrac{0.152(1-0.152)}{260}}}\approx 3.54808524246\approx3.55[/tex]

∴ The test statistic : z= 3.55