Question

question 9
the range of the correlation coefficient is from 0 to 1.
true
false
question 10
a recent survey indicated that the average amount spent for breakfast by business managers was $7.58 with a standard deviation of $0.42. it was felt that breakfasts on the west coast were higher than $7.58. a sample of 81 business managers on the west coast had an average breakfast cost of $7.65. with an \\(\alpha = 0.01\\), find the \\(p\\)-value for the test.
a. 0.0668
b. 0.1325
c. 0.4332
d. 0.2734
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Explanation:

Step1: Calculate the test - statistic \(z\)

The formula for the \(z\) - statistic in a one - sample mean test is \(z=\frac{\bar{x}-\mu}{\frac{\sigma}{\sqrt{n}}}\).
Here, \(\bar{x} = 7.65\), \(\mu=7.58\), \(\sigma = 0.42\), and \(n = 81\).
First, calculate \(\frac{\sigma}{\sqrt{n}}=\frac{0.42}{\sqrt{81}}=\frac{0.42}{9}=0.0467\).
Then, \(z=\frac{7.65 - 7.58}{0.0467}=\frac{0.07}{0.0467}\approx1.5\).

Step2: Find the \(P\) - value

Since this is a right - tailed test (because we are testing if the value is higher), the \(P\) - value is \(P(Z>z)\).
Using the standard normal distribution table, \(P(Z > 1.5)=1 - P(Z\leq1.5)\).
From the standard normal table, \(P(Z\leq1.5)=0.9332\).
So, \(P(Z>1.5)=1 - 0.9332 = 0.0668\).

Answer:

A. \(0.0668\)