Consider the probability distribution of x, where x is the number of job applications completed by a college senior through the
1 answer:
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Answer:
A.the type 1 error probability is
B. β = 0.0122
C. β = 0.0000
Step-by-step explanation:
Given that:
Mean = 100
standard deviation = 2
sample size = 9
The null and the alternative hypothesis can be computed as follows:
A. If the acceptance region is defined as , find the type I error probability
.
Assuming the critical region lies within or
, for a type 1 error to take place, then the sample average x will be within the critical region when the true mean heat evolved is
∴
when
From the standard normal distribution tables
Thus, the type 1 error probability is
B. Find beta for the case where the true mean heat evolved is 103.
The probability of type II error is represented by β. Type II error implies that we fail to reject null hypothesis
Thus;
β = P( type II error) - P( fail to reject )
∴
Given that
From standard normal distribution table
β = 0.0122 - 0.0000
β = 0.0122
C. Find beta for the case where the true mean heat evolved is 105. This value of beta is smaller than the one found in part (b) above. Why?
Given that
From standard normal distribution table
β = 0.0000 - 0.0000
β = 0.0000
The reason why the value of beta is smaller here is that since the difference between the value for the true mean and the hypothesized value increases, the probability of type II error decreases.
Answer:
a) The 98% confidence interval for the mean weight is between 10.00409 grams and 10.00471 grams
b) 49 measurements are needed.
Step-by-step explanation:
Question a:
We have that to find our level, that is the subtraction of 1 by the confidence interval divided by 2. So:
Now, we have to find z in the Ztable as such z has a pvalue of .
That is z with a pvalue of , so Z = 2.327.
Now, find the margin of error M as such
In which is the standard deviation of the population and n is the size of the sample.
The lower end of the interval is the sample mean subtracted by M. So it is 10.0044 - 0.00031 = 10.00409 grams
The upper end of the interval is the sample mean added to M. So it is 10 + 0.00031 = 10.00471 grams
The 98% confidence interval for the mean weight is between 10.00409 grams and 10.00471 grams.
(b) How many measurements must be averaged to get a margin of error of +/- 0.0001 with 98% confidence?
We have to find n for which M = 0.0001. So
Rounding up
49 measurements are needed.
The answer is negative 5
Answer:
1. Alexa traveled at a faster rate because the slope of her line is , which is greater than the slope of the line described by the data in Mia’s table.
Step-by-step explanation:
We know that,
Slope of and
is
Mia records the distance traveled over the time by the table.
Taking the points (10,5) and (18,9), the slope is given by,
Mia's slope =
i.e. Mia's slope =
i.e. Mia's slope =
Alexa records the distance traveled over the time by the graph.
Taking the points (4,3) and (8,6), the slope is given by,
Alexa's slope =
i.e. Alexa's slope =
As, Alexa's slope = >
= Mia's slope.
So, the correct option is,
1. Alexa traveled at a faster rate because the slope of her line is , which is greater than the slope of the line described by the data in Mia’s table.