According to the Vivino website, suppose the mean price for a bottle of red wine that scores 4.0 or higher on the Vivino Rating System is $32.48. A New England-based lifestyle magazine wants to determine if red wines of the same quality are less expensive in Providence, and it has collected prices for 61 randomly selected red wines of similar quality from wine stores throughout Providence. The mean and standard deviation for this sample are $30.15 and $12, respectively.
(a) Develop appropriate hypotheses for a test to determine whether the sample data support the conclusion that the mean price in Providence for a bottle of red wine that scores 4.0 or higher on the Vivino Rating System is less than the population mean of $32.48. (Enter != for ≠ as needed.)

(b) Using the sample from the 60 bottles, what is the test statistic? (Round your answer to three decimal places.)

Using the sample from the 60 bottles, what is the p-value? (Round your answer to four decimal places.)

(c) At α = 0.05, what is your conclusion?

There is not enough evidence to support the claim that the mean price in Providence for a bottle of red wine that scores 4.0 or higher on the Vivino Rating System is less than the population mean of $32.48.

Step-by-step explanation:

We are given the following in the question:

Population mean, μ = $32.48

Sample mean, [tex]\bar{x}[/tex] = $30.15

Sample size, n = 60

Sample standard deviation, s = $12

a) First, we design the null and the alternate hypothesis

[tex]H_{0}: \mu \geq 32.48\text{ dollars}\\H_A: \mu < 32.48\text{ dollars}[/tex]

We use one-tailed t test to perform this hypothesis.

b) Formula:

[tex]t_{stat} = \displaystyle\frac{\bar{x} - \mu}{\frac{s}{\sqrt{n}} }[/tex]

Putting all the values, we have

[tex]t_{stat} = \displaystyle\frac{30.15 - 32.48}{\frac{12}{\sqrt{61}} } = -1.516[/tex]

Now, [tex]t_{critical} \text{ at 0.05 level of significance, 59 degree of freedom } = -1.671[/tex]

Calculating the p-value from table, we get,

P-value = 0.06743

Since, the calculated p-value is greater than the significance level, we fail to reject the null hypothesis and accept it.

c) Thus, there is not enough evidence to support the claim that the mean price in Providence for a bottle of red wine that scores 4.0 or higher on the Vivino Rating System is less than the population mean of $32.48.

AFOKE88 AFOKE88 · Answer 2 · 2021-10-28T12:32:36+02:00

A)The appropriate hypotheses for this test is;

Null Hypothesis; H₀; μ ≥ 34.28

Alternative Hypothesis; Hₐ; μ < 34.38

B) The test statistic and p-value for this test respectively are;

z = -1.516 and p-value = 0.06476

C) At α = 0.05, the conclusion of the sample test is that;

There is no sufficient evidence to support the claim that the mean price in Providence for a bottle of red wine that scores 4.0 or higher on the Vivino Rating System is less than the population mean of $32.48.

We are given;

Population mean; μ = $32.48

Sample size; n = 61

Sample mean; x' = $30.15

Standard deviation; σ = $12

A) Let us define the hypotheses;

Null Hypothesis; H₀; μ ≥ 34.28

Alternative Hypothesis; Hₐ; μ < 34.38

B) Let us find the test statistic from the formula;

z = (x' - μ)/(σ/√n)

z = (30.15 - 32.48)/(12/√61)

z = -1.516

From online p-value from z-score calculator attached, using z = -1.516, α = 0.05 and one tailed hypothesis, we have;

p-value = 0.06476

C) The p-value is greater than the significance value and as such we conclude that; there no sufficient evidence to support the claim that the mean price in Providence for a bottle of red wine that scores 4.0 or higher on the Vivino Rating System is less than the population mean of $32.48.

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