Answer:
We conclude that the effectiveness is less than the 85% claim the company is making.
Step-by-step explanation:
We are given that a manufacturer of a new medication on the market for Crohn's disease makes a claim that the medication is effective in 85% of people who have the disease.
One hundred seventy-five individuals with Crohn's disease are given the medication, and 135 of them note the medication was effective.
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<em>Let p = </em><u><em>percentage of people who have the Crohn's disease.</em></u>
So, Null Hypothesis, : p = 85% {means that the effectiveness is equal to the 85% claim the company is making}
Alternate Hypothesis, : p < 85% {means that the effectiveness is less than the 85% claim the company is making}
The test statistics that would be used here <u>One-sample z proportion</u> <u>statistics</u>;
T.S. = ~ N(0,1)
where, = sample proportion of individuals who note the medication was effective = = 0.77
n = sample of individuals with Crohn's disease taken = 175
So, <em><u>test statistics</u></em> =
= -2.515
The value of z test statistics is -2.515.
<em>Now, at 0.05 significance level the z table gives critical value of -1.645 for left-tailed test.</em>
<em>Since our test statistic is less than the critical value of z as -2.515 < -1.645, so we have sufficient evidence to reject our null hypothesis as it will fall in the rejection region due to which </em><u><em>we reject our null hypothesis</em></u><em>.</em>
Therefore, we conclude that the effectiveness is less than the 85% claim the company is making.