Answer:
b. It will decrease by a factor of 2
Step-by-step explanation:
In a sample with a number n of people surveyed with a probability of a success of 
, and a confidence interval 
, we have the following confidence interval of proportions.
In which
z is the zscore that has a pvalue of 
.
The lower end of the interval is given by:
The upper end of the interval is given by:
The length of the interval is the subtraction of the upper end by the lower end, so it is:
This means that the length is inverse proportional to the square root of the size of the sample.
So, if the sample size is multiplied by 4, the length of the interval is going to decrease by a factor of 2.
Answer:
I think Its D
Step-by-step explanation:
Not sure tho
Answer:
Step-by-step explanation:
Hello!
So you have a new type of shoe that lasts presumably longer than the ones that are on the market. So your study variable is:
X: "Lifetime of one shoe pair of the new model"
Applying CLT:
X[bar]≈N(μ;σ²/n)
Known values:
n= 30 shoe pairs
x[bar]: 17 months
S= 5.5 months
Since you have to prove whether the new shoes last more or less than the old ones your statistical hypothesis are:
H₀:μ=15
H₁:μ≠15
The significance level for the test is given: α: 0.05
Your critical region will be two-tailed:
So you'll reject the null Hypothesis if your calculated value is ≤-1.96 or if it is ≥1.96
Now you calculate your observed Z-value
Z=<u>x[bar]-μ</u> ⇒ Z=<u> 17-15 </u> = 1.99
σ/√n 5.5/√30
Since this value is greater than the right critical value, i.e. Zobs(1.99)>1.96 you reject the null Hypothesis. So the average durability of the new shoe model is different than 15 months.
I hope you have a SUPER day!
