A study by Consumer Reports showed that 64% of supermarket shoppers believe supermarket brands to be as good as national name brands. To investigate whether this result applies to its own product, the manufacturer of a national name-brand ketchup asked a sample of shoppers whether they believed that supermarket ketchup was as good as the national brand ketchup. A random sample of 350 shoppers showed that 217 thought the supermarket brand was as good as the national brand. Should we conduct a one or two tail test in this situation?

So the p value obtained was a very high value and using the significance level given we have so we can conclude that we have enough evidence to FAIL reject the null hypothesis.

Step-by-step explanation:

She need to conduct a two tailed hypothesis test since she want to check if the standar dof 0.64 for the proportion is satisfied.

Data given and notation

n=350 represent the random sample taken

X=217 represent the shoppers who thought the supermarket brand was as good as the national brand

estimated proportion of shoppers who thought the supermarket brand was as good as the national brand

is the value that we want to test

represent the significance level

Confidence=95% or 0.95 (assumed)

z would represent the statistic (variable of interest)

represent the p value (variable of interest)  

Concepts and formulas to use  

We need to conduct a hypothesis in order to test the claim that the true proportion of shoppers who thought the supermarket brand was as good as the national brand is 0.64.:  

Null hypothesis:  

Alternative hypothesis:  

When we conduct a proportion test we need to use the z statistic, and the is given by:  

(1)  

The One-Sample Proportion Test is used to assess whether a population proportion is significantly different from a hypothesized value .

Calculate the statistic  

Since we have all the info requires we can replace in formula (1) like this:  

Statistical decision  

It's important to refresh the p value method or p value approach . "This method is about determining "likely" or "unlikely" by determining the probability assuming the null hypothesis were true of observing a more extreme test statistic in the direction of the alternative hypothesis than the one observed". Or in other words is just a method to have an statistical decision to fail to reject or reject the null hypothesis.  

The significance level provided . The next step would be calculate the p value for this test.  

Since is a bilateral test the p value would be:  

So the p value obtained was a very high value and using the significance level given we have so we can conclude that we have enough evidence to FAIL reject the null hypothesis.