Would you rather ... Drive a car at a rate of 40 miles per hour ***OR*** Drive a car at a rate of 50 feet per second?
2 answers:
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Answer:
The 95% confidence interval for the true mean speed of thunderstorms is [10.712, 13.688].
Step-by-step explanation:
Given information:
Sample size = 10
Sample mean = 12.2 mph
Standard deviation = 2.4
Confidence interval = 95%
At confidence interval 95% then z-score is 1.96.
The 95% confidence interval for the true mean speed of thunderstorms is
Where, is sample mean, z* is z score at 95% confidence interval, s is standard deviation of sample and n is sample size.
Therefore the 95% confidence interval for the true mean speed of thunderstorms is [10.712, 13.688].
Answer:
the probability of a Type II error if in fact the mean waiting time u, is 9.8 minutes is 0.1251
Option A) is the correct answer.
Step-by-step explanation:
Given the data in the question;
we know that a type 11 error occur when a null hypothesis is false and we fail to reject it.
as in it in the question;
obtained mean is 9.8 which is obviously not equal to 8.3
But still we fail to reject the null hypothesis says mean is 8.3
Hence we have to find the probability of type 11 error
given that; it is right tailed and o.5, it corresponds to 1.645
so
z is equal to 1.645
z = (x-μ)/
where our standard deviation s = 3.8
sample size n = 50
mean μ = 8.3
we substitute
1.645 = (x - 8.3)/
1.645 = (x - 8.3) / 0.5374
0.884023 = x - 8.3
x = 0.884023 + 8.3
x = 9.18402
so, by general rule we will fail to reject the null hypothesis when we will get the z value less than 1.645
As we reject the null hypothesis for right tailed test when the obtained test statistics is greater than the critical value
so, we will fail to reject the null hypothesis as long as we get the sample mean less than 9.18402
Now, for mean 9.8 and standard deviation 3.8 and sample size 50
Z = (9.18402 - 9.8)/
Z = -0.61598 / 0.5374
Z = - 1.1462 ≈ - 1.15
from the z-score table;
P(z<-1.15) = 0.1251
Therefore, the probability of a Type II error if in fact the mean waiting time u, is 9.8 minutes is 0.1251
Option A) is the correct answer.