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Mathematics

2 answers:

lisov135 [29]3 years ago

6 0

Answer:

Step-by-step explanation:

mr_godi [17]3 years ago

4 0

Answer:

b i copy cause i dont know

Step-by-step explanation:

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4 years ago

1. A researcher would like to learn about the difference in proportions of students and faculty who support textbook price caps.

Colt1911 [192]

Answer: (0.186, 0.298)

Step-by-step explanation:

The formula to find the confidence interval for the difference of the population proportion is given by :-

$\hat{p}_1-\hat{p}_2\pm z^*\sqrt{\dfrac{\hat{p}_1(1-\hat{p}_1)}{n_1}+\dfrac{\hat{p}_2(1-\hat{p}_2)}{n_2}}$ ... (i)

, where $n_1=$ Sample size of population 1.

$n_2=$ Sample size of population 2.

$\hat{p_1}=$ Sample proportion of population 1.

$\hat{p}_2$ = Sample proportion of population 2.

z* = Critical z-value corresponding to confidence interval

As per given , we have

$n_1=n_2=500$

$\hat{p}_1=\dfrac{378}{500}=0.756\\\hat{p}_2=\dfrac{256}{500}=0.512$

Critical value corresponds to 95% confidence interval = 1.96

Put all these values , in (i) , we get

$0.756-0.512\pm 1.96\sqrt{\dfrac{0.756(1-0.756)}{500}+\dfrac{0.512(1-0.512)}{500}}\\\\=0.244\pm1.96(\sqrt{0.00086864})\\\\=0.244\pm1.96(0.0294727)\\\\=0.244\pm0.0577665\\\\=(0.244-0.0577664,\ 0.24+0.0577664)\\\\=(0.1862336,\ 0.2977664)\approx(0.186,\ 0.298)$