An element with mass 430 grams decays by 27.4% per minute. How much of the element is remaining after 19 minutes, to the nearest
1 answer:
The equation for exponential decay is 
, where <em>a</em> is the initial amount, <em>b</em> = 1 + <em>r</em> (the growth rate as a decimal number) and <em>x</em> is the number of time periods (in this case, minutes). Substituting the information we have:
. To the nearest tenth of a gram, this would be 1.0 grams.
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Answer:
So the answer for this case would be n=238 rounded up to the nearest integer
Null hypothesis:
Alternative hypothesis:
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, and we can't conclude that the true mean is lower than 247 at 10% of significance.
Step-by-step explanation:
For this case we have the following data given:
represent the sample mean
represent the population deviation
represent the sample size selected
represent the value that we want to test.
The standard error for this case is given by:
For the 90% confidence the value of the significance is given by and
so we can find in the normal standard distribution a quantile that accumulates 0.05 of the area on each tail and we got:
And the margin of error would be:
The confidence interval for this case would be given by:
The margin of error is given by this formula:
(a)
And on this case we have that ME =5 and we are interested in order to find the value of n, if we solve n from equation (a) we got:
(b)
Replacing into formula (b) we got:
So the answer for this case would be n=238 rounded up to the nearest integer
State the null and alternative hypotheses.
We need to conduct a hypothesis in order to check if the true mean is lower than 247 pounds, the system of hypothesis would be:
Null hypothesis:
Alternative hypothesis:
Since we know the population deviation, 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 left tailed 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, and we can't conclude that the true mean is lower than 247 at 10% of significance.