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Please be guided with the notes below the questions.

HYPOTHESIS-TESTING

CASE:

According to the Okavanggo website, the mean price for a bottle of red wine that scores 4.0 or higher on the Okavanggo 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 56 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.

REQUIRED:

1.Determine the hypothesis test to be used by identifying the test variable and the grouping variable.

Determine which statistical test is to be used based on whether it is a test of comparison or test of relationship, the number of groupings and the level of measurement scale.

2.Formulate the appropriate Ho & Ha in either traditional or operational manner as well as in numerical form to determine if 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 Okavanggo Rating System is less than the population mean of $32.48.

EXAMPLE:

Traditional or Conventional Manner:

Ho: There is no significant difference in the mean age of the two groups. (the italics can be changed to any of the test variables and grouping variable)

Ha: There is a significant difference in the mean age of the two groups. (the italics can be changed to any of the test variables and grouping variable)

Ho: There is no relationship between quantity demanded and price of the good.

Ha: There is a relationship between quantity demanded and price of the good.

Operational or Conversational Manner:

Ho: The mean age of the two groups are the same. (the italics can be changed to any of the test variables and grouping variable)

Ha: The mean age of the two groups are not the same.(the italics can be changed to any of the test variables and grouping variable)

Ho: Quantity demanded is independent from the price of the good.

Ha: Quantity demanded is dependent on the price of the good.

NUMERICAL MANNER:

H_0: greater than or equal to 32.48

(_{1 2})

H_a: is less than 32.48 (₁ < ₂)

3.Make the statistical decision assuming that the p-value is 0.0475.

Specify the level of significance or alpha, .

The level establishes a criterion, or "cut-off", or acceptance region for making a decision about the null hypothesis. The alpha level also determines the risk of a Type I error. The default is at 5%.

* If it is a two-tailed test, divide the level of significance by 2.

4.Formulate the statistical conclusion.

Using the critical value approach:

Compare the critical or tabular value with the test statistic or computed value.

Accept or Retain the null hypothesis (Ho), if the test statistic or computed value is lesser or equal to the tabular or critical value. Otherwise, do not accept the null and instead accept the alternative hypothesis.

Low computed values or low test statistic values are likely to occur in the acceptance region of the Ho.

Using the p-value approach:

Compare the level of significance with the p-value.

Accept or Retain the null hypothesis (Ho), if the p-value is greater or equal to the level of significance.

Otherwise, do not accept the null and instead accept the alternative hypothesis.

High p-values imply the high occurrence or probability of Ho to happen.

Interpret or make the statistical conclusion based on the given problem or in the context of the application.