500% as a decimal and fraction
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Answer:
As the pvalue of the test is 0.02097 < 0.1, using a .10 significance level, he can conclude that the average trunk diameter of a pine tree is greater than the average diameter of a spruce tree.
Step-by-step explanation:
Using a .10 significance level, can he conclude that the average trunk diameter of a pine tree is greater than the average diameter of a spruce tree
The null hypothesis is that they are equal(that is, subtraction between the means is 0), while the alternate hypothesis is that they are greater(that is, subtraction between the means is larger than 0). So
In which is the mean pine trees height while
is the mean spruce trees height.
The test statistic is:
In which X is the sample mean, is the value tested at the null hypothesis and s is the standard error.
0 is tested at the null hypothesis:
This means that
Mean trunk diameter (cm) 35 30:
Pine trees - 35
Spruce trees - 30
The sample mean is given by the subtraction of the means. So
Sample Size 40 80
Population variance 160 160
This means that the standard error for each sample is given by:
The standard error of the difference is the square root of the sum squared of the standard error of each sample.
Test statistic:
Pvalue of the test:
Probability of a sample mean larger than 5, which is 1 subtracted by the pvalue of Z when X = 5.
Looking at the z-table, z = 2.04 has a pvalue of 0.9793.
1 - 0.9793 = 0.0207
As the pvalue of the test is 0.02097 < 0.1, using a .10 significance level, he can conclude that the average trunk diameter of a pine tree is greater than the average diameter of a spruce tree.
Answer:
represent the sample for the sample 1
represent the sample for the sample 2
represent the deviation for the sample 1
represent the deviation for the sample 2
represent the sample size for the group 1
represent the sample size for the group 2
And on this case if we create the system of hypothesis we have this:
Null hypothesis :
Alternative hypothesis:
Step-by-step explanation:
Previous concepts
A hypothesis is defined as "a speculation or theory based on insufficient evidence that lends itself to further testing and experimentation. With further testing, a hypothesis can usually be proven true or false".
The null hypothesis is defined as "a hypothesis that says there is no statistical significance between the two variables in the hypothesis. It is the hypothesis that the researcher is trying to disprove".
The alternative hypothesis is "just the inverse, or opposite, of the null hypothesis. It is the hypothesis that researcher is trying to prove".
On this caseHe wants to prove that Raymondville residents (population 1) dine out more often than Rosenberg residents (population 2). So this statement need to be on the alternative hypothesis. And the complement of the alternative hypothesis would be on the null hypothesis.
Solution to the problem
We assume that we have the following statistics:
represent the sample for the sample 1
represent the sample for the sample 2
represent the deviation for the sample 1
represent the deviation for the sample 2
represent the sample size for the group 1
represent the sample size for the group 2
And on this case if we create the system of hypothesis we have this:
Null hypothesis :
Alternative hypothesis: