Joe Ortega is the product manager for Ole ice cream. You...

Joe Ortega is the product manager for Ole ice cream. You have been asked to determine if Ole ice cream has greater sales than Carl's ice cream, which is a strong competitor. The data file Ole contains weekly sales and price data for the competing brands over the year in three different supermarket chains. These sample data represent a random sample of all ice cream sales for the two brands. The variable names clearly identify the variables. a. Design and implement an analysis to determine if there is strong evidence to conclude that Ole ice cream has higher mean sales than Carl's ice cream $(\alpha=0.05)$. Explain your procedure and show all computations. You may include Minitab output if appropriate to support your analysis. Explain your conclusions. b. Design and implement an analysis to determine if the prices charged for the two brands are different $(\alpha=0.05)$. Carefully explain your analysis, show all computations, and interpret your results.

Joe Ortega is the product manager for Ole ice cream. You have been asked to determine if Ole ice cream has greater sales than Carl's ice cream, which is a strong competitor. The data file Ole contains weekly sales and price data for the competing brands over the year in three different supermarket chains. These sample data represent a random sample of all ice cream sales for the two brands. The variable names clearly identify the variables.
a. Design and implement an analysis to determine if there is strong evidence to conclude that Ole ice cream has higher mean sales than Carl's ice cream $(\alpha=0.05)$. Explain your procedure and show all computations. You may include Minitab output if appropriate to support your analysis. Explain your conclusions.
b. Design and implement an analysis to determine if the prices charged for the two brands are different $(\alpha=0.05)$. Carefully explain your analysis, show all computations, and interpret your results.

Key Concepts

Significance Level

The significance level, commonly denoted as ?, is the pre-determined threshold for deciding when to reject the null hypothesis. It represents the probability of making a Type I error—that is, rejecting the null hypothesis when it is actually true. A common significance level used in tests is 0.05.

Hypothesis Testing

Hypothesis testing is a systematic method used in statistics to evaluate whether there is enough evidence in a sample of data to infer that a certain condition is true for the entire population. It involves stating a null hypothesis (a statement of no effect or difference) and an alternative hypothesis (what you want to test for), then using sample data to determine whether or not to reject the null hypothesis.

Null and Alternative Hypotheses

The null hypothesis typically represents a baseline or status quo assumption, such as there being no difference between two population means, while the alternative hypothesis represents the claim or difference to be tested. Clearly formulating these hypotheses is critical for determining the outcome of a statistical test.

Two-sample t-test

A two-sample t-test is a statistical method used to compare the means of two independent groups to determine whether there is a significant difference between them. This test is particularly useful when the sample sizes are small and when data are assumed to be approximately normally distributed.

P-value

The p-value is the probability of obtaining a test statistic at least as extreme as the one computed from the sample data, assuming that the null hypothesis is true. A small p-value indicates that such an extreme observed result is unlikely under the null hypothesis, leading researchers to reject the null hypothesis in favor of the alternative.

Assumptions for t-tests

When conducting a two-sample t-test, it is important to consider its underlying assumptions: the samples should be independent, the data should be approximately normally distributed, and if equal variances are assumed, the variances of the populations should be similar. Verifying these assumptions helps ensure the validity of the test’s results.

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