a boat costs $16600 and decreased in value by 14% per year. How much will the boat be worth after 11 years?
1 answer:
The worth of boat after 11 years is $ 3159.3013
<em><u>Solution:</u></em>
Given that,
Boat costs $16600 and decreased in value by 14% per year
To find: Worth of boat after 11 years
<em><u>The formula for decreasing function is given as:</u></em>
Where,
y is the value after "t" years
t is the number of years
a is the initial value
r is decreasing rate in decimal
<em><u>From given,</u></em>
a = 16600
t = 11
<em><u>Substituting the values we get,</u></em>
Thus the worth of boat after 11 years is $ 3159.3013
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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 to reject the null hypothesis, so we can conclude that the true mean is different from 1 pound at 5% of signficance.
Step-by-step explanation:
Data given and notation
represent the sample mean
represent the population standard deviation
sample size
represent the value that we want to test
represent the significance level for the hypothesis test.
z 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 true mean is equal to 1 pound or no :
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 two-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 to reject the null hypothesis, so we can conclude that the true mean is different from 1 pound at 5% of signficance.