Help me plz. You have to evaluate the expression.
1 answer:
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To start this question, we should know what is the atomic number of cobalt. The atomic number (the number of protons) of Cobalt is Z =27.
Now, we know that a Cobalt 60 isotope means an isotope of Cobalt whose Atomic Mass is 60.
Thus, in a Cobalt 60 isotope, the number of neutrons in the nucleus are
From the question we know that the given nuclear mass is 59.933820 u.
Now, the mass defect of Cobalt 60 can be easily calculated by adding the masses of the protons and the neutrons as per our calculations and subtracting the given nuclear mass from it.
Thus,
Mass Defect = (Number of Protons Mass of Proton given in the question) + (Number of Neutrons Mass of Neutron given in the question)-59.933820 u
Thus, the required Mass Defect is 0.5634u.
In eV, the Mass Defect is
Answer:
If we compare the p value and the significance level assumed we see that
so we can conclude that we have enough evidence to fail reject the null hypothesis, so we can't conclude that the true mean is different from 0.5 at 5% of signficance. So then the claim makes sense
Step-by-step explanation:
Previous concepts
A confidence interval is "a range of values that’s likely to include a population value with a certain degree of confidence. It is often expressed a % whereby a population means lies between an upper and lower interval".
The margin of error is the range of values below and above the sample statistic in a confidence interval.
Normal distribution, is a "probability distribution that is symmetric about the mean, showing that data near the mean are more frequent in occurrence than data far from the mean".
represent the sample mean for the sample
population mean (variable of interest)
s represent the sample standard deviation
n represent the sample size
Solution to the problem
In order to calculate the mean and the sample deviation we can use the following formulas:
(2)
(3)
The mean calculated for this case is
The sample deviation calculated
We need to conduct a hypothesis in order to check if the true mean is 0.5 or no, the system of hypothesis would be:
Null hypothesis:
Alternative hypothesis:
If we analyze the size for the sample is < 30 and we don't know the population deviation so is better apply a t test to compare the actual mean to the reference value, and the statistic is given by:
(1)
t-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
The first step is calculate the degrees of freedom, on this case:
Since is a two sided test the p value would be:
Conclusion
If we compare the p value and the significance level assumed we see that
so we can conclude that we have enough evidence to fail reject the null hypothesis, so we can't conclude that the true mean is different from 0.5 at 5% of signficance. So then the claim makes sense