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rewona [7]
3 years ago
9

One hundred draws are made at random with replacement from box A, and 250 are made at random with replacement from box B. (a) 50

of the draws from box A are positive, compared to 131 from box B: 50.0% versus 52.4%. Is this difference real, or due to chance
Mathematics
1 answer:
Yuliya22 [10]3 years ago
3 0

Answer:

Therefore WE accept the Null hypothesis H_0 That 50.0% versus 52.4%.difference is real

Step-by-step explanation:

Sample size A n_a=100

Sample size B n_b=250

Positive draw from box A n_a=50

Positive draw from box b n_b=131

Generally the equation for Probability of Positive draw from Box A is mathematically given by

 P_1=\frac{50}{100}

 P_1=50%

Therefore

 1-P_1=50\%

Generally the equation for Probability of Positive draw from Box A is mathematically given by

 P_1=\frac{131}{250}

 P_1=52.4%

Therefore

 1-P_1=47.6\%

Generally the equation for Standard error S.E is mathematically given by

 S.E=\sqrt{\frac{n_1(p_1)*(1-P_1)}{n_1^2}+\frac{n_2(P_2(1-p^2))}{n_2^2}}

 S.E=\sqrt{\frac{100(0.50)*(50)}{100^2}+\frac{(250)(0.524(47))}{250^2}}

 S.E=0.592

 S.E=59.2\%

Therefore

 Z=\frac{50-52.4}{59.2}

Generally

 P value P>0.05

Therefore WE accept the Null hypothesis H_0 That 50.0% versus 52.4%.difference is real

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