Which of the following is equivalent to the expression below?
1 answer:
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Answer:
Step-by-step explanation:
Hello!
The study variables are:
: The number of Brand A units sold that required repair.
: THe number of Brand B units sold that required repair.
1. Calculate the difference in the sample proportion for the two brands of computers, p^BrandA−p^BrandB =?.
The sample proportion of each sample is equal to the number of "success" observed xi divided by the sample size n:
^p=
^p=
^p - ^p
= 0.1328 - 0.1502= -0.0174
Note: proportions take numbers from 0 to 1, meaning they are always positive. But this time what you have to calculate is a difference between the two proportions so it is absolutely correct to reach a negative number it just means that one sample proportion is greater than the other.
2. What are the correct hypotheses for conducting a hypothesis test to determine whether the proportion of computers needing repairs is different for the two brands?
A. H0:pA−pB=0 , HA:pA−pB<0
B. H0:pA−pB=0 , HA:pA−pB>0
C. H0:pA−pB=0 , HA:pA−pB≠0
If you want to test whether the proportion of computers of both brands is different, you have to do a two-tailed test, the correct option is C.
3. Calculate the pooled estimate of the sample proportion, ^p= ?
To calculate the pooled sample proportion you have to use the following formula:
^p=
4. Is the success-failure condition met for this scenario?
A. Yes
B. No
The conditions that have to be met are:
⇒ Met
⇒ 836 * 0.1328= 111.4192; Met
⇒ 836 * (1 - 0.1328)= 727.5808; Met
⇒ Met
⇒ 739 * 0.1502= 110.9978; Met
⇒ 739 * (1-0.1502)= 628.0022; Met
All conditions are met.
5. Calculate the test statistic for this hypothesis test. ? =
6. Calculate the p-value for this hypothesis test, p-value = .
This hypothesis test is two-tailed and so is the p-value, since it has two tails you have to calculate it as:
P(Z≤-0.9902) + P(Z≥0.9902)= P(Z≤-0.9902) + ( 1 - P(Z≤0.9902))= 0.161 + (1 - 0.839) = 0.322
7. What is your conclusion using α = 0.05?
A. Do not reject H0
B. Reject H0
The decision rule using th ep-value is:
If p-value > α, the decision is to not reject the null hypothesis.
If p-value ≤ α, the decision is to reject the null hypothesis.
The p-value= 0.322 is greater than α = 0.05, so the decision is to not reject the null hypothesis.
8. Compute a 95 % confidence interval for the difference p^BrandA−p^BrandB = ( , )
The formula to calculate the Confidence interval is a little different, because instead of the pooled sample proportion you have to use the sample proportion of each sample to calculate the standard deviation of the distribution:
() ±
*
-0.0174 ± 1.965 *
[-0.0520; 0.0172]
I hope it helps!