Choose correct answer for the following: a. POPT Popcorn is trying to determine
ID: 3323149 • Letter: C
Question
Choose correct answer for the following:
a. POPT Popcorn is trying to determine the percentage of kernels of popcorn that will pop with the maximum error of 1.7%. How many kernels must be sampled to meet this requirement at the 95% confidence level?
Choose correct answer for the following:
a. POPT Popcorn is trying to determine the percentage of kernels of popcorn that will pop with the maximum error of 1.7%. How many kernels must be sampled to meet this requirement at the 95% confidence level?
A. 29 B. 58 C. 2341 D. 3324 b. In a marketing survey, a random sample of 925 shoppers revealed that 705 remained loyal to their favorite supermarkets during the past year. Find a 95% confidence interval for the percentage of people who will remain loyal to their supermarket. A. .79 B. .73 C. .87 D. .77 c. The US census reported that it takes workers an average of 35 minutes to drive home from work. City officials in Los Angles believe that it takes workers in their city, on average, greater than or equal to 35 minutes to drive home from work. Which of the following gives the proper null hypothesis to test the claim that the average length of time for workers in LA to drive home from work is at least 35 minutes? A. u=35 B. u<35 C. u>35 D. u!=35 d. It is claimed that the national average for the price of gasoline in $2.66 per gallon. A sample of 25 gas stations in Hays yielded a sample mean of $2.89, and it is known that national standard deviation is =0.48. Compute the test statistic for this test A. 1.982 B. 2.396 C. 2.251 D. 1.00Explanation / Answer
a.
Compute Sample Size ( n ) = n=(Z/E)^2*p*(1-p)
Z a/2 at 0.05 is = 1.96
Sample Proportion = 0.5
ME = 0.017
n = ( 1.96 / 0.017 )^2 * 0.5*0.5
= 3323.2 ~ 3324
option:D
b.
TRADITIONAL METHOD
given that,
possibile chances (x)=705
sample size(n)=925
success rate ( p )= x/n = 0.76
I.
sample proportion = 0.76
standard error = Sqrt ( (0.76*0.24) /925) )
= 0.01
II.
margin of error = Z a/2 * (stanadard error)
where,
Za/2 = Z-table value
level of significance, = 0.05
from standard normal table, two tailed z /2 =1.96
margin of error = 1.96 * 0.01
= 0.03
III.
CI = [ p ± margin of error ]
confidence interval = [0.76 ± 0.03]
= [ 0.73 , 0.79]
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DIRECT METHOD
given that,
possibile chances (x)=705
sample size(n)=925
success rate ( p )= x/n = 0.76
CI = confidence interval
confidence interval = [ 0.76 ± 1.96 * Sqrt ( (0.76*0.24) /925) ) ]
= [0.76 - 1.96 * Sqrt ( (0.76*0.24) /925) , 0.76 + 1.96 * Sqrt ( (0.76*0.24) /925) ]
= [0.73 , 0.79] =(73%,79%)
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interpretations:
1. We are 95% sure that the interval [ 0.73 , 0.79] contains the true population proportion
2. If a large number of samples are collected, and a confidence interval is created
for each sample, 95% of these intervals will contains the true population proportion
c.
City officials in Los Angles believe that it takes workers in their city,
on average, greater than or equal to 35 minutes to drive home from work
null hypothesis Ho:U<=35
alternative hypothesis Ha:U>=35
d.
Given that,
population mean(u)=2.66
standard deviation, =0.48
sample mean, x =2.89
number (n)=25
null, Ho: =2.66
alternate, H1: !=2.66
level of significance, = 0.05
from standard normal table, two tailed z /2 =1.96
since our test is two-tailed
reject Ho, if zo < -1.96 OR if zo > 1.96
we use test statistic (z) = x-u/(s.d/sqrt(n))
zo = 2.89-2.66/(0.48/sqrt(25)
zo = 2.396
| zo | = 2.396
critical value
the value of |z | at los 5% is 1.96
we got |zo| =2.396 & | z | = 1.96
make decision
hence value of | zo | > | z | and here we reject Ho
p-value : two tailed ( double the one tail ) - ha : ( p != 2.396 ) = 0.017
hence value of p0.05 > 0.017, here we reject Ho
ANSWERS
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null, Ho: =2.66
alternate, H1: !=2.66
test statistic: 2.396
critical value: -1.96 , 1.96
decision: reject Ho
p-value: 0.017
option:B