What is the standard form of the line through the given point: (3,5), with slope = -3
1 answer:
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Answer:
a. Mean
b. μ = μ₀
c. 11.5%
d. Yes
Step-by-step explanation:
The given parameters are;
The mean work week for engineers, μ₀ = 63 hours
The standard deviation, σ = 5 hours
The number of engineers in Kara's sample, n = 10 engineers
The responses given by the 10 engineers are;
70; 45; 55; 60; 65; 55; 55; 60; 50; 55
a. The given information which the newly hired is hoping to find out that it is not is the <em>mean</em>
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b. The null hypothesis which is that the company claim is correct, is therefore;
Null hypothesis, H₀; μ = μ₀ = 63 hours
c. Kara's mean, is found as follows;
= (70 + 45 + 55 + 60 + 65 + 55 + 55 + 60 + 50 + 55)/10 = 57
= 57 hours
The Z-score is therefore;
Z = (57 - 63)/5 = -1.2
From the Z-table, we have;
The p-value for P( ≤ 57) = P(Z ≤ -1.2) = 0.11507
The probability as a percentage given to one decimal place, that the mean would be as low as Kara's mean, P( ≤ 57) = 11.5%
d. Given that the percent percentage chance (11.5%) that the mean could be as low as hers ( = 57 hours) is higher than 10%, she should accept the claim.
Answer:
Comparing the p value with the significance level provided we see that
so we can conclude that we have enough evidence to reject the null hypothesis, and a would be a significant difference in the average of the two groups.
Step-by-step explanation:
Assuming the following info
IT Training N mean Stdev
In-house 210 $490 $32
Consultants 180 $500 $48
1) Data given and notation
represent the mean for the sample of In-house
represent the mean for the sample Consutants
represent the population standard deviation for the sample In-house
represent the population standard deviation for the sample Consultants
sample size for the group In-house
sample size for the group Consultants
t would represent the statistic (variable of interest)
2) Concepts and formulas to use
We need to conduct a hypothesis in order to check if the means for the two groups are the same, the system of hypothesis would be:
Null hypothesis:
Alternative hypothesis:
We don't have the population standard deviation's, so for this case is better apply a t test to compare means, and the statistic is given by:
(1)
t-test: Is used to compare group means. Is one of the most common tests and is used to determine whether the means of two groups are equal to each other.
3) Calculate the statistic
With the info given we can replace in formula (1) like this:
4) Statistical decision
First we need to calculate the degrees of freedom given by:
Comparing the p value with the significance level provided we see that
so we can conclude that we have enough evidence to reject the null hypothesis, and a would be a significant difference in the average of the two groups.