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3 years ago

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Pennsylvania Refining Company is studying the relationship between the pump price of gasoline and the number of gallons sold. Fo

r a sample of 14 stations last Tuesday, the correlation was 0.65. Can the company conclude that the correlation is positive

1 answer:

Semenov [28]3 years ago

6 0

Complete Question

Pennsylvania Refining Company is studying the relationship between the pump price of gasoline and the number of gallons sold. For a sample of 14 stations last Tuesday, the correlation was 0.65.At the 0.01 significance level Can the company conclude that the correlation is positive

Answer:

Yes the company conclude that the correlation is positive

Step-by-step explanation:

From the question we are told that

The sample size is n = 14

The correlation is r = 0.65

The null hypothesis is $H_o : r < 0$

The alternative hypothesis is $H_1 : r > 0$

Generally the standard deviation is mathematically evaluated as

$Sr = \sqrt{1- r}$

$Sr = \sqrt{1- 0.65}$

$Sr = 0.616$

The degree of freedom for the one-tail test is

$df = n- 2$

$df = 14- 2$

$df = 12$

The standard error is evaluated as

$SE = \frac{0.616}{ \sqrt{12} }$

$SE =0.1779$

The test statistics is evaluated as

$t = \frac{r }{SE}$

$t = \frac{0.65 }{0.1779}$

$t = 3.654$

The p-value of of t is obtained from the z table, the value is

$p-value = P(t < 3.654) = 0.00012909$

Given that $p-value < \alpha$ then we reject the null hypothesis

Hence the company can conclude that the correlation is positive

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Answer:

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b) The minimum sample size is 2401.

Step-by-step explanation:

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In which

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For this problem, we have that:

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$n = 600.25$

Rounding up

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b. If a 95% confidence interval with a margin of error of no more than 0.02 is desired, give a close estimate of the minimum sample size necessary to achieve the desired margin of error.

Now we want n for which M = 0.02. So

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$\sqrt{n} = \frac{1.96*0.5}{0.02}$

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Answer:

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Step-by-step explanation:

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