Answer:
Decision rule for rejecting is
reject H0 is test statistic <-1.233
Step-by-step explanation:
Given that a sample of 1300 computer chips revealed that 27% of the chips do not fail in the first 1000 hours of their use, as against company literature of 29%
To test this we create hypotheses as
![H_0: p = 29%\\H_a: p](https://tex.z-dn.net/?f=H_0%3A%20p%20%3D%2029%25%5C%5CH_a%3A%20p%20%3C27%25)
(left tailed test at 10% significance level)
p difference = -0.02
STd error of p = ![\sqrt{0.29*0.71/1300} \\=0.0126](https://tex.z-dn.net/?f=%5Csqrt%7B0.29%2A0.71%2F1300%7D%20%5C%5C%3D0.0126)
Test statistic = p diff/std error = -0.1587
For 10% significance level for right tailed test we can reject H0 if
test statistic <-1.645
Decision rule for rejecting is
reject H0 is test statistic <-1.233
Answer:
negative correlation
Step-by-step explanation:
Answer:
65.827% of the apples have diameter between 3.5 and 4.3 inches.
Step-by-step explanation:
Problems of normally distributed samples can be solved using the z-score formula.
In a set with mean
and standard deviation
, the zscore of a measure X is given by
![Z = \frac{X - \mu}{\sigma}](https://tex.z-dn.net/?f=Z%20%3D%20%5Cfrac%7BX%20-%20%5Cmu%7D%7B%5Csigma%7D)
After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X.
So, to find the proportion of apples with diameter between 3.5 and 4.3 inches, we subtract the pvalue of the zscore of X = 4.3 by the pvalue of the zscore of X = 3.5.
The diameters of apples from a certain farm follow normal distribution with mean 4 inches and standard deviation 0.4 inch. So
,
.
For X = 4.3
![Z = \frac{X - \mu}{\sigma}](https://tex.z-dn.net/?f=Z%20%3D%20%5Cfrac%7BX%20-%20%5Cmu%7D%7B%5Csigma%7D)
![Z = \frac{4.3 - 4}{0.4}](https://tex.z-dn.net/?f=Z%20%3D%20%5Cfrac%7B4.3%20-%204%7D%7B0.4%7D)
![Z = 0.75](https://tex.z-dn.net/?f=Z%20%3D%200.75)
Z = 0.75 has a pvalue of 0.77337
For X = 3.5
![Z = \frac{X - \mu}{\sigma}](https://tex.z-dn.net/?f=Z%20%3D%20%5Cfrac%7BX%20-%20%5Cmu%7D%7B%5Csigma%7D)
![Z = \frac{3.5 - 4}{0.4}](https://tex.z-dn.net/?f=Z%20%3D%20%5Cfrac%7B3.5%20-%204%7D%7B0.4%7D)
![Z = -1.20](https://tex.z-dn.net/?f=Z%20%3D%20-1.20)
Z = -1.20 has a pvalue of 0.1151
Subtracting
![0.77337 - 0.1151 = 0.65827](https://tex.z-dn.net/?f=0.77337%20-%200.1151%20%3D%200.65827)
65.827% of the apples have diameter between 3.5 and 4.3 inches.
Answer:
(0,-2)
Step-by-step explanation:
the answer is (0,-2) because -2 is where the line crosses over the y-axis. If we looked at a graph you would see that the line goes over 0 on the X-axis, which causes the line to touch the y-axis and intercept it at the -2 mark.
An easy way to find the answer for these sorts of questions is to draw out a graph and mark the coordinates on it and draw the line conecting them. Once you've done that you can easily see where the line intercepts on both the y and x axis.
Answer:
There are 12 red fish, 19 orange fish
Step-by-step explanation:
Let y rep amount of red fish
y + 7 = Amount of orange fish
y + y + 7 = 31
2y = 31 - 7
2y = 24
y = 12
Then
y + 7
12 + 7 = 19