Q20

Mitchell works in the produce section at a small local supermarket and would like to test whether the proportion of apples people purchase is the same for each season, using a significance level of 0.01. He analyzes the apple purchases each season for a year and records his findings in the following table. Season Spring Summer Fall Winter Total ----- - - --- # of apples purchased 1226 1328 1328 1225 5107 (a) In performing this statistical test, state the hypotheses. Ho: the distribution of apples people purchased is the same for each season vs. Ha: the distribution of apples people purchased is not the same for each season Ho: the total number of apples people purchased is not the same for each season vs. Ha: the total number of apples people purchased is the same for each season Ho: the observed number of apples people purchased is the same for each season vs. Ha: the observed number of apples people purchased is not the same for each season Ho: the distribution of apples people purchased is not the same for each season vs. Ha: the distribution of apples people purchased is the same for each season Ho: the proportion of customers is the same each season vs. Ha: the proportion of customers is not the same each season (b) What is the expected number of apples purchased for each season? Fill out the table. (Round your answers to 2 decimal places, if needed.) ------ Spring Summer Fall Winter (c) What is the test statistic value for this hypothesis test? (Round your answers to 2 decimal places, if needed.) TS = (d) The test statistic follows a t-distribution with of = 4 (e) Using the statistical table, the p-value is p-value > 0.10 (f) Based on the p-value, those conducting the test should fail to reject * the null hypothesis at the significance level of 0.01. (9) What is the appropriate conclusion? There is sufficient evidence to conclude the total number of customers for each season are not all the same. O There is insufficient evidence to conclude the total number of customers for each season are not all the same. There is insufficient evidence to conclude the distribution of apples purchased is not the same for each season. O There is sufficient evidence to conclude the distribution of customers apples purchased is the same for each season. There is sufficient evidence to conclude the distribution of apples purchased is not the same for each season