Marjorie bought 24 bottles of juice. She drinks 2 bottles each day. Which of the following best represents the number of bottles
1 answer:
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Answer: the median is 6.
Please see the picture attached.
A line plot shows the number of occurrences (crosses) of each number of a data set.
The median is the central value, the middle number, of a data set ordered from least to greatest. When there are two middle numbers, the median will be the mean between the two.
In order to find the median, look at the line plot: count how many values you have (22), then add 1 (23) and divide by two (11.5). Since we have an even number of values, we will have two middle numbers, which will be in the eleventh and twelfth position.
Count the crosses from the left, the eleventh and twelfth crosses both correspond to the number 6, therefore the median is 6.
You can also write all the numbers in increasing order and divide them into two equal groups:
1, 2, 3, 3, 4, 4, 5, 5, 5, 6, 6 | 6, 6, 7, 7, 7, 8, 8, 8, 9, 9, 11
The median will be the average between the two central numbers, therefore 6 (again).
Please see the picture attached.
A line plot shows the number of occurrences (crosses) of each number of a data set.
The median is the central value, the middle number, of a data set ordered from least to greatest. When there are two middle numbers, the median will be the mean between the two.
In order to find the median, look at the line plot: count how many values you have (22), then add 1 (23) and divide by two (11.5). Since we have an even number of values, we will have two middle numbers, which will be in the eleventh and twelfth position.
Count the crosses from the left, the eleventh and twelfth crosses both correspond to the number 6, therefore the median is 6.
You can also write all the numbers in increasing order and divide them into two equal groups:
1, 2, 3, 3, 4, 4, 5, 5, 5, 6, 6 | 6, 6, 7, 7, 7, 8, 8, 8, 9, 9, 11
The median will be the average between the two central numbers, therefore 6 (again).
Answer:
a) One-tailed t-test about a mean.
b) The null hypothesis would be that there is no significant evidence to conclude that the adjusted grip leads to more distance on the thrown ball.
While the alternative hypothesis is that there is significant evidence to conclude that the adjusted grip leads to more distance on the thrown ball.
Mathematically,
The null hypothesis is represented as
H₀: μ ≤ 40 yards
The alternative hypothesis is given as
Hₐ: μ > 40 yards
c) p-value = 0.00621
d) The graph is presented in the attached image. The p-value obtained is less than the significance level at which the test was performed, hence, we accept the alternative hypothesis and say that there is significant evidence to conclude that the adjusted grip leads to more distance on the thrown ball.
Step-by-step explanation:
a) This test checks if the adjusted grip leads to more distance than before on the ball throws.
So, it is a one tailed test (testing only in one direction), a t-test about a mean.
b) For hypothesis testing, the first thing to define is the null and alternative hypothesis.
The null hypothesis plays the devil's advocate and usually takes the form of the opposite of the theory to be tested. It usually contains the signs =, ≤ and ≥ depending on the directions of the test.
While, the alternative hypothesis usually confirms the the theory being tested by the experimental setup. It usually contains the signs ≠, < and > depending on the directions of the test.
Since this question aims to test if adjusting the grip leads to more distance on the ball thrown.
The null hypothesis would be that there is no significant evidence to conclude that the adjusted grip leads to more distance on the thrown ball. That is, The adjusted grip leads to a distance lesser than or equal to the previous distance on the thrown ball.
While the alternative hypothesis is that there is significant evidence to conclude that the adjusted grip leads to more distance on the thrown ball.
Mathematically,
The null hypothesis is represented as
H₀: μ ≤ 40 yards
The alternative hypothesis is given as
Hₐ: μ > 40 yards
c) To do this test, we will use the z-distribution because there is information on the population standard deviation.
So, we compute the test statistic
z = (x - μ₀)/σ
x = 45 yards
μ₀ = 40 yards
σ = standard deviation = 2 yards
z = (45 - 40)/2 = 2.50
The p-value for a one-tailed test for z-test statistic of 2.50 is 0.00621
d) The sketch of the graph is presented in the attached image.
The interpretation of p-values is that
When the (p-value > significance level), we fail to reject the null hypothesis and when the (p-value < significance level), we reject the null hypothesis and accept the alternative hypothesis.
So, for this question, significance level = 0.05
p-value = 0.00621
0.00621 < 0.05
Hence,
p-value < significance level
This means that we reject the null hypothesis & accept the alternative hypothesis and say that there is enough evidence to conclude that the adjusted grip leads to more distance on the thrown ball.
Hope this Helps!!!
