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kipiarov [429]
2 years ago
7

A study sampled 350 upperclassmen (Group 1) and 250 underclassmen (Group 2) at high schools around the city of Houston. The stud

y was performed at the end of the school year and asked each if they had used steroids at any point in the last school year. Of the upperclassmen, 25 claimed to have used steroids in the last school year, and of the underclassmen, 19 claimed to have used steroids. Run a 95% confidence interval to test for a significant difference in the proportions of students who used steroids.
Mathematics
1 answer:
iris [78.8K]2 years ago
6 0

Answer:

-0.048

Do not reject  H_0:P_1-P_2=0

Step-by-step explanation:

From the question we are told that

Sample size n_1=350

Sample size n_2=250

Sample proportion 1  \hat P= \frac{25}{350} =>0.07

Sample proportion 2 \hat P= \frac{19}{250} =>0.076

95% confidence interval

Generally for 95% confidence level

Level of significance

 \alpha = 1-0.95=>0.05

 \alpha /2=\frac{0.05}{2} =>0.025

Therefore

Z_a_/_2=1.96

Generally the equation for confidence interval between P_1 - P_2  is mathematically given as

(\hat P_1-\hat P_2)\pm Z_a_/_2\sqrt{\frac{\hat P_1(1-\hat P_1)}{n_1}+\frac{\hat P_2(1-\hat P_2)}{n_2}  }

(0.07-0.076)\pm 1.96\sqrt{\frac{0.07(1-0.07)}{350}+\frac{0.076(1-0.076)}{250}  }

(0.07-0.076)\pm 1.96\sqrt{4.66896*10^-^4  }

(-0.006)\pm 0.042

(-0.006)- 0.042=>-0.048

(-0.006)+ 0.042=>0.036

Therefore

Confidence interval is

-0.048

Conclusion

Given the confidence interval has zero

Therefore do not reject  H_0:P_1-P_2=0

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