Answer:
We accept the null hypothesis and the population mean is $120.
Step-by-step explanation:
We are given the following in the question:
Sample size, n = 100
Sample mean, 
= $120
Alpha, α = 0.01
Sample standard deviation, s = $25
First, we design the null and the alternate hypothesis
We use two-tailed t test to perform this hypothesis.
Formula:
Putting all the values, we have
p-value one tail= 0.024
p-value two tail= 0.048
Conclusion:
Since the p-value for two tailed test is greater than the significance level, we fail to reject the null hypothesis and accept it.
Thus, the population mean is $120.
Answer:
<u>Marge's</u> present age = 14 ; <u>Dan's</u> present age = 29
Step-by-step explanation:
Let Marge's present age be = M
Dan's present age [D] : 14 years elder than Marge = M + 14
Marge Age = M - 8
Dan's Age = D - 8 = (M + 14) - 8 = M + 6
{Given} : Dan's age = 3 times Marge's age
M + 6 = 3 (M - 8)
M + 6 = 3M - 24
6 + 24 = 3M - M
30 = 2M
M = 30/2
M = 15 [Marge's present age]
Dan's present age [D] = M + 14 = 29
Complex solutions, namely roots with a √(-1) or "i" in it, never come all by their lonesome, because an EVEN root like the square root, can have two roots that will yield the same radicand.
a good example for that will be √(4), well, (2)(2) is 4, so 2 is a root, but (-2)(-2) is also 4, therefore -2 is also a root, so you'd always get a pair of valid roots from an even root, like 2 or 4 or 6 and so on.
therefore, complex solutions or roots are never by their lonesome, their sister the conjugate is always with them, so if there's a root a + bi, her sister a - bi is also coming along too.
if complex solutions come in pairs, well, clearly a cubic equation can't yield 3 only.
To calculate the costs of a quart of strawberries and a quart of raspberries, use the two given condition to set-up an equation. Since two variables are unknown, it needs two equation to calculate the solution. Let x be the cost of a quart of strawberries and y as the cost of a quart of raspberries. So, 1st equation is 3x + 2y = 22, and 2nd equation is 5x + 4y = 39. Substitute one equation into the other by expressing one variable into another variable. Then, the answer is x = $3.5 and y = $5.75.
Answer:
infinity
Step-by-step explanation:
a) the expected value of this gamble in dollars is Infinity
i.e
expected value = 
= 
b)
When offered, most people say they would pay only less than $10 to play this game.
What are two reasons why people are willing to pay so much less than the expected value?
These people are ready to pay less than $10 to play this game due to the fact that people usually overlook the unlikely event when making decisions. In a bid to that logic, they gamble in order to double their amount of money and the probability that heads may never come is ignored by these people and they may hope for a likely event i.e a head every time they play the game.
Also, the expected value is so humongous that if and only if that the first head appears after a long series of tails which is very less certain to occur, because mostly people would think that on an average the length of a series of tails ( or heads) is somewhat near 10 or so, but definitely infinity.
