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Average age of a purchaser of doritos salsa verde

1. It was stated in the background that 63% of all US Hispanics are Mexican American. Suppose 850 US Hispanics are randomly selected using US Census Bureau information. 575 state that they are Mexican American. Test the population proportion at the 5% significance level.

2. What proportion of Hispanics listen primarily to ads in Spanish? Suppose one source says that in the past the proportion has been about 0.83. A random sample of 438 Hispanics is selected and 347 said they listen primarily to ads in Spanish. Test the past proportion at the 5% significance level.

3. What is the average age of a purchaser of Doritos Salsa Verde? Suppose initial tests indicate it is 31 years. A researcher wants to test this at the 1% significance level. She contacts 24 purchasers of Doritos Salsa Verde and finds that their mean age is 28.81 years with standard deviation 7.09. Assuming that the ages of purchasers are normally distributed in the population, what can the researcher conclude?

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Assume that the ANOVA assumptions are verified. State the rejection rule to test whether the population mean differs using ?