Given:
The coordinates of point K' are (6,5).
K' is the image of K after a reflection in the line y=2.
To find:
The coordinates of point K.
Solution:
Let the coordinates of point K are (a,b).
If a figure is reflected over the line y=2, then
Using this formula, the coordinates of image of K are
The coordinates of point K' are (6,5).
On comparing both sides, we get
Therefore, the coordinates of point K are (6,-1).
Answer:
a) 0.280
b) 0.300
c) No, preference is not independent of gender. Since the P(N) (0.29) is not equal to P(N|M) (0.28) and/or P(N|F) (0.30), the preference and gender are not completely, statistically independent. It's very close though.
Step-by-step explanation:
Let the probability that the somebody surveyed is a male be P(M)
Let the probability that somebody surveyed is female be P(F)
Let the probability that somebody surveyed picked the name-brand milk be P(N)
Let the probability that somebody surveyed picked the store-brand milk be P(St)
Let the probability that somebody surveyed picked the something else be P(So)
a) Given that an American is a male, what is the probability that he prefers name-brand milk = P(N|M) = 319/1138 = 0.280
b) Given that an American is a female, what is the probability that she prefers name-brand milk = P(N|F) = 341/1138 = 0.300
c) To investigate if the preference and gender are independent or not, we need the P(N)
P(N) = probability that an average an Average American (male or female) will prefer a nam-brand milk = 660/2276 = 0.290.
Since the P(N) (0.29) is not equal to P(N|M) (0.28) and/or P(N|F) (0.30), the preference and gender are not statistically independent. It's very close though.
Answer:
We accept the null hypothesis, that is, that the mean weight of the cans is still of 12 ounces of fruit.
Step-by-step explanation:
Pineapple Corporation (PC) maintains that their cans have always contained an average of 12 ounces of fruit.
This means that the null hypothesis is:
The production group believes that the mean weight has changed.
This means that the alternate hypothesis is:
The test statistic is:
In which X is the sample mean, is the value tested at the null hypothesis,
is the standard deviation and n is the size of the sample.
12 is tested at the null hypothesis:
This means that
They take a sample of 15 cans and find a sample mean of 12.05 ounces and a sample standard deviation of .08 ounces.
This means, respectibely, that
Value of the test statistic:
Pvalue of the test:
We are testing if the mean is different from a value, which means that the pvalue is 2 multiplied by 1 subtracted by the pvalue of z = 2.42.
Looking at the z-table, z = 2.42 has a pvalue of 0.9922
1 - 0.9922 = 0.0078
2*0.0078 = 0.0156
What conclusion can we make from the appropriate hypothesis test at the .01 level of significance?
0.0156 > 0.01. This means that at the 0.01 level, we accept the null hypothesis, that is, that the mean weight of the cans is still of 12 ounces of fruit.