What fraction is equivalent to 84/100?
1 answer:
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Answer:
If we compare the p value and the significance level given we see that
so we can conclude that we have enough evidence to FAIL to reject the null hypothesis, so we can't conclude that the true mean is not significantly higher than 200 at 5% of signficance.
Step-by-step explanation:
Data given and notation
represent the mean height for the sample
represent the population standard deviation
sample size
represent the value that we want to test
represent the significance level for the hypothesis test.
t would represent the statistic (variable of interest)
represent the p value for the test (variable of interest)
State the null and alternative hypotheses.
We need to conduct a hypothesis in order to check if the mean is higher than 200, the system of hypothesis would be:
Null hypothesis:
Alternative hypothesis:
If we analyze the size for the sample is < 30 but we know the population deviation so is better apply a z test to compare the actual mean to the reference value, and the statistic is given by:
(1)
z-test: "Is used to compare group means. Is one of the most common tests and is used to determine if the mean is (higher, less or not equal) to an specified value".
Calculate the statistic
We can replace in formula (1) the info given like this:
P-value
Since is a one sided test the p value would be:
Conclusion
If we compare the p value and the significance level given we see that
so we can conclude that we have enough evidence to FAIL to reject the null hypothesis, so we can't conclude that the true mean is not significantly higher than 200 at 5% of signficance.
Answer:
B.The probability 0+ indicates that the probability is a very small positive value. It indicates that the event is possible, but very unlikely.
Step-by-step explanation:
Out of 1009 consumers a sample of 30 consumers is selected and asked the questions. So, the sample size is 30.
n = 30
Based on previous survey, 42% are comfortable with the drone. So in this sample, we can consider the probability of success to be 42%.
p = 42% = 0.42
q = 1 - p = 1 - 0.42 = 0.58
We want to find the probability of getting exactly 24 consumers who are comfortable with drones.
x = 24
Since, the sample size is fixed, the selections are independent and probability of success is constant, we can use the Binomial Probability to answer this problem. All the conditions of a Binomial Distribution are being satisfied.
According to the formula of Binomial Distribution, the probability of getting exactly x success among n trials is given as:
Using the values, we get:
Thus, the probability of getting exactly 24 consumers from a sample of 30 who are comfortable with drones is 0.00002, which is extremely small.
Since, the value of probability is a very small positive number, it indicates that event is possible but very unlikely. An impossible event has probability equal to 0.
Therefore, option B gives the correct answer.