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Answer:
(a) The value = 72.3 is 1.21 standard deviations below the null value of <em>μ</em>.
(b) The mean drying time of paint is not less than 74.
Step-by-step explanation:
The hypothesis for the single mean test is:
<em>H₀</em>: <em>μ</em> = 74 vs. <em>Hₐ</em>: μ < 74.
The information provided is:
<em>σ</em> = 7
<em>n</em> = 25
As the population standard deviation is known, we will use a <em>z</em>-test for single mean.
(a)
The <em>z</em>-score is a Normal distribution with mean 0 and variance 1. It is also defined as the number of standard deviations a raw score is from the mean.
The <em>z</em>-score for sample mean is given by:
If = 72.3 compute the corresponding <em>z</em>-score as follows:
Thus, the value = 72.3 is 1.21 standard deviations below the null value of <em>μ</em>.
(b)
So the test statistic is, <em>z</em> = -1.21.
Compute the <em>p</em>-value of the test as follows:
*Use a <em>z</em>-table.
The decision rule says to, reject the null hypothesis if the <em>p</em>-value is less than the significance level <em>α</em> = 0.01 and vice-versa.
<em>p</em>-value = 0.1131 < <em>α</em> = 0.01
The null hypothesis was failed to be rejected.
Thus, the mean drying time of paint is not less than 74.
Given function is
now we need to find the value of k such that function f(x) continuous everywhere.
We know that any function f(x) is continuous at point x=a if left hand limit and right hand limits at the point x=a are equal.
So we just need to find both left and right hand limits then set equal to each other to find the value of k
To find the left hand limit (LHD) we plug x=-4 into 3x+k
so LHD= 3(-4)+k
To find the Right hand limit (RHD) we plug x=-4 into
so RHD=
Now set both equal
k=-0.47
<u>Hence final answer is -0.47.</u>