Answer: she will be able to spend $980 on the bike.
Step-by-step explanation:
We would apply the formula for determining compound interest which is expressed as
A = P(1 + r/n)^nt
Where
A = total amount in the account at the end of t years
r represents the interest rate.
n represents the periodic interval at which it was compounded.
P represents the principal or initial amount deposited
From the information given,
P = $800
r = 7% = 7/100 = 0.07
n = 1 because it was compounded once in a year.
t = 3 years
Therefore,.
A = 800(1 + 0.07/1)^1 × 3
A = 800(1 + 0.07)^3
A = 800(1.07)^3
A = $980
The power of the test against the specific alternative is given by 1 minus the probability of making a Type II error. Therefore, the power is 0.86= 86%
In statistical hypothesis testing, the power of a test is the probability that it correctly rejects a null hypothesis when a specific alternative hypothesis is true. In this case, we are given that the test has a significance level of α = 0.01, which means that the test rejects the null hypothesis if the probability of obtaining the observed result, or one more extreme, under the null hypothesis is less than 0.01.
However, we also know that when a specific alternative hypothesis is true, the test has a probability of making a Type II error of 0.14. This means that there is a 14% chance that the test fails to reject the null hypothesis, even though the alternative hypothesis is true.
Therefore, the power of the test against this specific alternative hypothesis is given by 1 minus the probability of making a Type II error, which is:
Power = 1 - P(Type II error) = 1 - 0.14 = 0.86
So, the power of the test against the specific alternative hypothesis is 0.86 or 86%. This means that when the alternative hypothesis is true, the test correctly rejects the null hypothesis 86% of the time.
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Answer:
421 3/50 - 212 9/10 = 208.16 or 5204/25
Step-by-step explanation:
To solve the expressions you could change the values into an improper fraction to solve easily
421 3/50 - 212 9/10 =
421 3/50 = 421 × 50 + 3 / 50 = 21053/50
212 9/10 = 212 × 10 + 9 / 10 = 2129/10
subtract the fractions as follows
21053/50 - 2129/10 =
common factor of the denominator is 50
21053 - 10645 / 50 =
subtract 10645 from 21053
10408/50 = 5204/25 in fraction or 208.16 in decimal