6. Amy bought some used books for $4.95. She paid $0.50 each for some books and $0.35 each for the others. She bought fewer than
1 answer:
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Answer:
So the p value obtained was a very high value and using the significance level given we have
so we can conclude that we have enough evidence to FAIL to reject the null hypothesis, and we can say that the true proportion not differs significantly from the specified value of 0.00034 or 0.034%.
Step-by-step explanation:
1) Data given and notation
n=420095 represent the random sample taken
X=135 represent the subjects developed cancer of the brain or nervous system (based on data from the Journal of the National Cancer Institute as reported in USA Today)
estimated proportion of subjects developed cancer of the brain or nervous system (based on data from the Journal of the National Cancer Institute as reported in USA Today)
is the value that we want to test
represent the significance level
Confidence=99.5% or 0.995
z would represent the statistic (variable of interest)
represent the p value (variable of interest)
2) Concepts and formulas to use
We need to conduct a hypothesis in order to test the claim that the brain or nervous system at a rate that is different from the rate of 0.0340% :
Null hypothesis:
Alternative hypothesis:
When we conduct a proportion test we need to use the z statistic, and the is given by:
(1)
The One-Sample Proportion Test is used to assess whether a population proportion is significantly different from a hypothesized value
.
3) Calculate the statistic
Since we have all the info requires we can replace in formula (1) like this:
4) Statistical decision
It's important to refresh the p value method or p value approach . "This method is about determining "likely" or "unlikely" by determining the probability assuming the null hypothesis were true of observing a more extreme test statistic in the direction of the alternative hypothesis than the one observed". Or in other words is just a method to have an statistical decision to fail to reject or reject the null hypothesis.
The significance level provided . The next step would be calculate the p value for this test.
Since is a bilateral test the p value would be:
So the p value obtained was a very high value and using the significance level given we have
so we can conclude that we have enough evidence to FAIL to reject the null hypothesis, and we can say that the true proportion not differs significantly from the specified value of 0.00034 or 0.034%.
Answer:
height = 7 cm
Step-by-step explanation:
The area (A) of a trapezium is calculated using the formula
A = h(a + b)
where h is the height and a, b the parallel bases
here a = 6, b = 12 and A = 63, hence
× h × (6 + 12) = 63
h × 18 = 63
9h = 63 ( divide both sides by 9 )
h = 7
<h3>Answer: </h3>
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Explanation:
The data set for Ali is
8.3, 5.9, 8.3, 8.9, 7.7, 7.2, 8.1, 9.1, 9.8, 5.8,
8.3, 4.7, 7.0, 6.5, 6.5, 8.4, 8.8, 8.1, 8.9, 9.9
which when on a single line looks like this
8.3, 5.9, 8.3, 8.9, 7.7, 7.2, 8.1, 9.1, 9.8, 5.8, 8.3, 4.7, 7.0, 6.5, 6.5, 8.4, 8.8, 8.1, 8.9, 9.9
Let's sort the values from smallest to largest
4.7, 5.8, 5.9, 6.5, 6.5, 7.0, 7.2, 7.7, 8.1, 8.1, 8.3, 8.3, 8.3, 8.4, 8.8, 8.9, 8.9, 9.1, 9.8, 9.9
Now lets break the data up into separate rows such that each time we get to a new units value, we move to another row
4.7
5.8, 5.9
6.5, 6.5
7.0, 7.2, 7.7
8.1, 8.1, 8.3, 8.3, 8.3, 8.4, 8.8, 8.9, 8.9
9.1, 9.8, 9.9
We have these stems: 4, 5, 6, 7, 8, 9 which represent the units digit of the values. The leaf values are the tenths decimal place.
For example, a number like 4.7 has a stem of 4 and leaf of 7 (as indicated by the key below)
This is what the stem-and-leaf plot looks like for Ali's data only
The stem-and-leaf plot condenses things by tossing out repeated elements. Instead of writing 8.1, 8.1, 8.3 for instance, we can just write a stem of 8 and then list the individual leaves 1, 1 and 3. We save ourselves from having to write two more copies of '8'
Through similar steps, this is what the stem-and-leaf plot looks like for Kumar's data set only
Kumar doesn't have any leaves for the stem 6, so we will have that section blank. It's important to have this stem so it aligns with Ali's stem plot.
Notice that both stem plots involve the same exact set of stems (4 through 9 inclusive).
What we can do is combine those two plots into one single diagram like this
Then the last thing to do is reverse each set of leaves for Ali (handle each row separately). The reason for this is so that each row of leaf values increases as you further move away from the stem. This is simply a style choice. This is somewhat similar to a number line, except negative values aren't involved here.
This is what the final answer would look like
The fact that Ali is on the left side vs Kumar on the right, doesn't really matter. We could swap the two positions and end up with the same basic table. I placed Ali on the left because her data set is on the top row of the original table given.
The thing you need to watch out for is that joining the stem and leaf for Ali means you'll have to read from right to left (as opposed to left to right). Always start with the stem. That's one potential drawback to a back-to-back stem-and-leaf plot. The advantage is that it helps us compare the two data sets fairly quickly.