Answer:
The proportion of student heights that are between 94.5 and 115.5 is 86.64%
Step-by-step explanation:
We have a mean and a standard deviation
. For a value x we compute the z-score as
, so, for x = 94.5 the z-score is (94.5-105)/7 = -1.5, and for x = 115.5 the z-score is (115.5-105)/7 = 1.5. We are looking for P(-1.5 < z < 1.5) = P(z < 1.5) - P(z < -1.5) = 0.9332 - 0.0668 = 0.8664. Therefore, the proportion of student heights that are between 94.5 and 115.5 is 86.64%
<u>Given</u>:
An Exhibitor is selling decorative wreaths at an arts and craft show.
The net profit P in dollars from the sales of the Wreaths is given by , where N is the number of wreaths sold.
We need to determine the number of wreaths sold to earn a net profit of $100.
<u>Number of wreaths sold:</u>
The number of wreaths sold to earn a profit of $100 can be determined by substituting P(n) = 100 in the equation , we get;
Thus, the number of wreaths sold is 200.
Answer:
If we compare the p value and the significance level given and we can see that
so we can conclude that we have enough evidence to FAIL reject the null hypothesis, so we can't conclude that the true average speed is lower than 25 mph at 5% of signficance.
Step-by-step explanation:
Data given and notation
represent the sample mean
represent the sample standard deviation
sample size
represent the value that we want to test
represent the significance level for the hypothesis test.
t would represent the statistic (variable of interest)
represent the p value for the test (variable of interest)
State the null and alternative hypotheses.
We need to conduct a hypothesis in order to check if the true mean for the average speed is lower than 25 mph, the system of hypothesis would be:
Null hypothesis:
Alternative hypothesis:
If we analyze the size for the sample is < 30 and we don't know the population deviation so is better apply a t test to compare the actual mean to the reference value, and the statistic is given by:
(1)
Calculate the statistic
We can replace in formula (1) the info given like this:
P-value
The first step is calculate the degrees of freedom, on this case:
Since is a one side test the p value would be:
Conclusion
If we compare the p value and the significance level given and we can see that
so we can conclude that we have enough evidence to FAIL reject the null hypothesis, so we can't conclude that the true average speed is lower than 25 mph at 5% of signficance.
Answer:
<em>a)95% confidence intervals for the population mean of light bulbs in this batch</em>
(325.5 ,374.5)
b)
<em>The calculated value Z = 4 > 1.96 at 0.05 level of significance</em>
<em>Null hypothesis is rejected </em>
<em>The manufacturer has not right to take the average life of the light bulbs is 400 hours.</em>
Step-by-step explanation:
Given sample size n = 64
Given mean of the sample x⁻ = 350
Standard deviation of the Population σ = 100 hours
The tabulated value Z₀.₉₅ = 1.96
<em>95% confidence intervals for the population mean of light bulbs in this batch</em>
<em></em><em></em>
<em></em><em></em>
(325.5 ,374.5)
b)
<u><em>Explanation</em></u>:-
Given mean of the Population μ = 400
Given sample size n = 64
Given mean of the sample x⁻ = 350
Standard deviation of the Population σ = 100 hours
<u><em>Null hypothesis</em></u> : H₀:The manufacturer has right to take the average life of the light bulbs is 400 hours.
μ = 400
<u><em>Alternative Hypothesis: H₁:</em></u> μ ≠400
<u><em>The test statistic </em></u>
|Z| = |-4|
The tabulated value Z₀.₉₅ = 1.96
The calculated value Z = 4 > 1.96 at 0.05 level of significance
Null hypothesis is rejected.
<u><em>Conclusion:</em></u>-
The manufacturer has not right to take the average life of the light bulbs is 400 hours.