Answer:
Step-by-step explanation:
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Answer:
The function f(x) is positive in the interval (-≠,-2.5) ∪ (1,∞)
Step-by-step explanation:
we have
This is a vertical parabola open upward (the leading coefficient is positive)
The vertex is a minimum
The coordinates of the vertex is the point (h,k)
step 1
Find the vertex of the quadratic function
Factor the leading coefficient 2
Complete the square
Rewrite as perfect squares
The vertex is the point (-\frac{3}{4},-\frac{49}{8})
step 2
Find the x-intercepts (values of x when the value of f(x) is equal to zero)
For f(x)=0
take the square root both sides
therefore
The function f(x) is negative in the interval (-2.5,1)
The function f(x) is positive in the interval (-≠,-2.5) ∪ (1,∞)
see the attached figure to better understand the problem
Answer:
(a) Null Hypothesis, :
= $24.57
Alternate Hypothesis, :
$24.57
(b) The P-value of the test statistics is 0.1212.
(c) We conclude that the population mean hourly wage in the manufacturing industry equals the population mean hourly wage in the U.S industries using P-value approach.
(d) We conclude that the population mean hourly wage in the manufacturing industry equals the population mean hourly wage in the U.S industries using critical value approach.
Step-by-step explanation:
We are given that a sample of employees from the manufacturing industry to see if the mean hourly wage differs from the reported mean of $24.57 for the U.S industries.
Suppose a sample of 30 employees from the manufacturing industry showed a sample mean of $23.89 per hour. Assume a population standard deviation of $2.40 per hour.
Let = <u><em>population mean hourly wage in the manufacturing industry.</em></u>
(a) Null Hypothesis, :
= $24.57 {means that the population mean hourly wage in the manufacturing industry equals the population mean hourly wage in the U.S industries}
Alternate Hypothesis, :
$24.57 {means that the population mean hourly wage in the manufacturing industry differs from the population mean hourly wage in the U.S industries}
The test statistics that would be used here <u>One-sample z test statistics</u> as we know about the population standard deviation;
T.S. = ~ N(0,1)
where, = sample mean wage in the manufacturing industry = $23.89/hr
σ = population standard deviation = $2.40/hr
n = sample of employees from the manufacturing industry = 30
So, <em><u>the test statistics</u></em> =
= -1.55
The value of z test statistics is -1.55.
(b) <u>Now, the P-value of the test statistics is given by;</u>
P-value = P(Z < -1.55) = 1 - P(Z 1.55)
= 1 - 0.9394 = 0.0606
For two-tailed test P-value is calculated as = 0.0606 2 = <u>0.1212</u>
Since, the P-value of the test statistics is higher than the level of significance as 0.1212 > 0.05, so we have insufficient evidence to reject our null hypothesis as it will not fall in the rejection region due to which <u>we fail to reject our null hypothesis</u>.
Therefore, we conclude that the population mean hourly wage in the manufacturing industry equals the population mean hourly wage in the U.S industries.
(d) <u>Now, at 0.05 significance level the z table gives critical values of -1.96 and 1.96 for two-tailed test.</u>
Since our test statistic lies within the range of critical values of z, so we have insufficient evidence to reject our null hypothesis as it will not fall in the rejection region due to which <u>we fail to reject our null hypothesis</u>.
Therefore, we conclude that the population mean hourly wage in the manufacturing industry equals the population mean hourly wage in the U.S industries.