Answer:
Step-by-step explanation:
Red:black = 1:1
Red cards = x
Black cards =x
x + x = 48
2x = 48
x = 48/2
x = 24
No. of red cards = 24
No of black cards = 24
Now 8 red cards are removed
So, No. of red cards = 24 - 8 =16
Red: Black = 16:24
Red: Black = 2:3
Answer:
There is no sufficient evidence to reject the company's claim at the significance level of 0.05
Step-by-step explanation:
Let be the true mean weight per apple the company ship. We want to test the next hypothesis
vs
(two-tailed test).
Because we have a large sample of size n = 49 apples randomly selected from a shipment, the test statistic is given by
which is normally distributed. The observed value is
. The rejection region for
is given by RR = {z| z < -1.96 or z > 1.96} where the area below -1.96 and under the standard normal density is 0.025; and the area above 1.96 and under the standard normal density is 0.025 as well. Because the observed value 1.4583 does not fall inside the rejection region RR, we fail to reject the null hypothesis.
Answer:
With 89.9% we can say that the mean improvement is between 583.1 and 728.1 vehicles per hour.
Step-by-step explanation:
We are given that the effectiveness of the new method was evaluated in a simulation study. In 50 simulations, the mean improvement in traffic flow in a particular intersection was 655.6 vehicles per hour, with a standard deviation of 311.7 vehicles per hour.
A traffic engineer states that the mean improvement is between 583.1 and 728.1 vehicles per hour.
<em>Let </em><em> = sample mean improvement</em>
The z-score probability distribution for sample mean is given by;
Z = ~ N(0,1)
where, = mean improvement = 655.6 vehicles per hour
= standard deviation = 311.7 vehicles per hour
n = sample of simulations = 50
The Z-score measures how many standard deviations the measure is away from the mean. After finding the Z-score, we look at the z-score table and find the p-value (area) associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X.
Now, Probability that the mean improvement is between 583.1 and 728.1 vehicles per hour is given by = P(583.1 < < 728.1) = P(
< 728.1) - P(
583.1)
P( < 728.1) = P(
<
) = P(Z < 1.64) = 0.9495
P(
583.1) = P(
) = P(Z
-1.64) = 1 - P(Z < 1.64)
= 1 - 0.9495 = 0.0505
<em />
<em>So, in the z table the P(Z </em><em> x) or P(Z < x) is given. So, the above probability is calculated by looking at the value of x = 1.64 in the z table which has an area of 0.9495.</em>
Therefore, P(583.1 < < 728.1) = 0.9495 - 0.0505 = 0.899 or 89.9%
Hence, with 89.9% we can say that the mean improvement is between 583.1 and 728.1 vehicles per hour.