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1 answer:
Answer:
Step-by-step explanation:
The general equation for a circle is the following:
Where (a, b) is the center of the circle and () is the radius of the circle. In order to shift the function to the right, one has to add to the (a) value; to move it to the left one has to subtract from it. Similarly, to move the function up, one has to add to the (b) value, to move it down, one has to subtract from it. Apply this to the given function:
The center of this circle is (-1, 2). The circle is shifted to the right by (3) units, and down by (4). Thus the center is also shifted by these values:
(-1, 2)
Right by (3): (-1 + 3) = 2
Down by (4): (2 - 4) = -2
Substitute back into the function:
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Answer:
a) Null hypothesis:
Alternative hypothesis:
b) the test statistics is : 2.15
c) The p-value is 0.0158
d) NO, there is evidence that the mean time of telephone survey is less than 15 and premium rate is not justified.
Step-by-step explanation:
The data in the Microsoft Excel are:
17;11;12;23;20;23;15;
16;23;22;18;23;25;14;
12;12;20;18;12;19;11;
11;20;21;11;18;14;13;
13;19; 16;10;22;18;23.
a) Formulate the null and alternative hypotheses for this application.
From the question, Fowle Marketing Research Inc. is taking base charge from a client on the given assumption that if the mean time of telephone survey is 15 minutes or less.
The null and alternative hypotheses are therefore as follows:
Null hypothesis:
The null hypothesis states that there is evidence that the mean time of telephone survey is less than 15 and premium rate is not justified.
Alternative hypothesis:
The alternative hypothesis states that there is evidence that the mean time of telephone survey exceeds 15 and premium rate is justified.
b) Compute the value of the test statistic.
Given that:
n = 35
The sample mean is;
Thus:
Thus; the test statistics is : 2.15
c) What is the p-value?
p-value = P(Z > 2.15)
p-value = 1 - P(Z ≤ 2.15)
From the standard normal table, the value of P(Z ≤ 2.15) is 0.9842
p-value = 1 - 0.9842
p-value = 0.0158
The p-value is 0.0158
d) At a = .01, what is your conclusion?
According to the rejection rule, if p-value is less than 0.01 then reject null hypothesis at ∝ = 0.01
Thus; p-value = 0.0158 > ∝ = 0.01
By the rejection rule, accept the null hypothesis.
Therefore, there is evidence that the mean time of telephone survey is less than 15 and premium rate is not justified.