A set of solar batteries is used in a research satellite. The satellite can run on only o the useful lifetime of the satellite before it goes dead. If the variance is too small, at Why? Engineers have determined that a variance of o? = 23 months (squared) is m (squared). Using a 0.05 level of significance, test the claim that o² = 23 against the (a) What is the level of significance? 0.05 State the null and alternate hypotheses. O H;: o² = 23; H,: o? < 23 Ho: o2 = 23; H,: o² + 23
Addition Rule of Probability
It simply refers to the likelihood of an event taking place whenever the occurrence of an event is uncertain. The probability of a single event can be calculated by dividing the number of successful trials of that event by the total number of trials.
Expected Value
When a large number of trials are performed for any random variable ‘X’, the predicted result is most likely the mean of all the outcomes for the random variable and it is known as expected value also known as expectation. The expected value, also known as the expectation, is denoted by: E(X).
Probability Distributions
Understanding probability is necessary to know the probability distributions. In statistics, probability is how the uncertainty of an event is measured. This event can be anything. The most common examples include tossing a coin, rolling a die, or choosing a card. Each of these events has multiple possibilities. Every such possibility is measured with the help of probability. To be more precise, the probability is used for calculating the occurrence of events that may or may not happen. Probability does not give sure results. Unless the probability of any event is 1, the different outcomes may or may not happen in real life, regardless of how less or how more their probability is.
Basic Probability
The simple definition of probability it is a chance of the occurrence of an event. It is defined in numerical form and the probability value is between 0 to 1. The probability value 0 indicates that there is no chance of that event occurring and the probability value 1 indicates that the event will occur. Sum of the probability value must be 1. The probability value is never a negative number. If it happens, then recheck the calculation.
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![W Math 2250 Unit 4 Post Test Re X
b Answered: (a) What is the level X +
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A set of solar batteries is used in a research satellite. The satellite can run on only one battery, but it runs best if more than one battery is used. The variance oʻ of lifetimes of these batteries affects
the useful lifetime of the satellite before it goes dead. If the variance is too small, all the batteries will tend to die at once. Why? If the variance is too large, the batteries are simply not dependable.
Why? Engineers have determined that a variance of o2
= 23 months (squared) is most desirable for these batteries. A random sample of 22 batteries gave a sample variance of 15.2 months
(squared). Using a 0.05 level of significance, test the claim that o?
= 23 against the claim that oʻ is different from 23.
(a) What is the level of significance?
0.05
State the null and alternate hypotheses.
Ho: o?
23; H;:
o2 < 23
Ho: o?
23; H1:
o2
+ 23
Ho:o?
23; H,: o² > 23
=
H: o2 > 23; H,: o2
= 23
(b) Find the value of the chi-square statistic for the sample. (Round your answer to two decimal places.)
13.88
What are the degrees of freedom?
21
What assumptions are you making about the original distribution?
We assume a binomial population distribution.
We assume a normal population distribution.
We assume a exponential population distribution.
We assume a uniform population distribution.
(c) Find or estimate the P-value of the sample test statistic.
P-value > 0.100
0.050 < P-value < 0.100
0.025 < P-value < 0.050
0.010 < P-value < 0.025
0.005 < P-value < 0.010
O P-value < 0.005](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F1f570524-1dae-4658-ab6a-e0258271edb8%2F353b32e6-3dc3-48ab-9caa-e2c1f16696f3%2Fs76rz6b_processed.png&w=3840&q=75)
![W Math 2250 Unit 4 Post Test Re X
b Answered: (a) What is the level X +
webassign.net/web/Student/Assignment-Responses/last?dep=24515412
What assumptions are you making about the original distribution?
We assume a binomial population distribution.
We assume a normal population distribution.
We assume a exponential population distribution.
We assume a uniform population distribution.
(c) Find or estimate the P-value of the sample test statistic.
P-value > 0.100
0.050 < P-value < 0.100
0.025 < P-value < 0.050
0.010 < P-value < 0.025
0.005 < P-value < 0.010
P-value < 0.005
(d) Based on your answers in parts (a) to (c), will you reject or fail to reject the null hypothesis?
Since the P-value > a, we fail to reject the null hypothesis.
Since the P-value > a, we reject the null hypothesis.
Since the P-value < a, we reject the null hypothesis.
Since the P-value < a, we fail to reject the null hypothesis.
(e) Interpret your conclusion in the context of the application.
At the 5% level of significance, there is insufficient evidence to conclude that the variance of battery life is different from 23.
At the 5% level of significance, there is sufficient evidence to conclude that the variance of battery life is different from 23.
(f) Find a 90% confidence interval for the population variance. (Round your answers to two decimal places.)
lower limit
upper limit
(g) Find a 90% confidence interval for the population standard deviation. (Round your answers to two decimal places.)
lower limit
months
upper limit
months
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