The Coca-Cola Company reported that the mean per capita...

The Coca-Cola Company reported that the mean per capita annual sales of its beverages in the United States was 423 eight-ounce servings (Coca-Cola Company website, February 3, 2009). Suppose you are curious whether the consumption of Coca-Cola beverages is higher in Adlanta, Georgia, the location of Coca-Cola's corporate headquarters. A sample of 36 individuals from the Allanta area showed a sample mean annual consumption of 460.4 eight-ounce servings with a standard devistion of $s=101.9$ ounces. Using $\alpha=.05$, do the sample results support the conclusion that mean annusal consumption of Coca-Cola beverage products is higher in Aulanta?

The Coca-Cola Company reported that the mean per capita annual sales of its beverages in the United States was 423 eight-ounce servings (Coca-Cola Company website, February 3,
2009). Suppose you are curious whether the consumption of Coca-Cola beverages is higher in Adlanta, Georgia, the location of Coca-Cola's corporate headquarters. A sample of 36 individuals from the Allanta area showed a sample mean annual consumption of 460.4 eight-ounce servings with a standard devistion of $s=101.9$ ounces. Using $\alpha=.05$, do the sample results support the conclusion that mean annusal consumption of Coca-Cola beverage products is higher in Aulanta?

Key Concepts

Test Statistic

The test statistic is a standardized value calculated from sample data during a hypothesis test. It quantifies the difference between the observed sample mean and the hypothesized population mean, relative to the variability in the sample data. In a one-sample t-test, the test statistic is computed by dividing the difference between the sample mean and the hypothesized mean by the standard error of the mean, and it is compared to a critical value from the t-distribution to decide whether to reject the null hypothesis.

Significance Level

The significance level, denoted by alpha (?), is the threshold for determining whether a test statistic is extreme enough to reject the null hypothesis. It represents the maximum acceptable probability of making a Type I error, which is rejecting a true null hypothesis. A common significance level used in hypothesis testing is 0.05, indicating a 5% risk of error.

Hypothesis Testing

Hypothesis testing is a statistical method used to make decisions or inferences about a population parameter based on sample data. It involves setting up a null hypothesis, which represents a baseline or status quo, and an alternative hypothesis, which represents the claim or effect the researcher wants to test. The test evaluates whether the observed data are sufficiently unlikely under the assumption that the null hypothesis is true.

One-Sample t-Test

A one-sample t-test is used when comparing the mean of a sample to a known value or a theoretical expectation for the population mean, especially when the population standard deviation is unknown. This test accounts for the variability in the sample by using the sample standard deviation, and it is appropriate when the sample size is relatively small or when the population distribution is assumed to be approximately normal.

T-Distribution

The t-distribution is a probability distribution that is used instead of the normal distribution when dealing with small sample sizes or when the population standard deviation is unknown. Its shape is similar to the normal distribution but has heavier tails, which means it gives more probability to extreme values. As the sample size increases, the t-distribution approaches the normal distribution.

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