some people claim that they can tell the difference between a diet soda and a regular soda in the first sip. a researcher wanting to test this claim randomly sampled 80 such people. he then filled 80 plain white cups with soda, half diet and half regular through random assignment, and asked each person to take one sip from their cup and identify the soda as diet or regular. 53 participants correctly identified the soda. do these data provide strong evidence that these people are any better than random guessing at telling the difference between diet and regular soda?

The lack of pattern or predictability in events, whether it be apparent or real, is referred to as randomness. Sometimes there is no order or discernible pattern or combination in a random series of events, symbols, or processes.

The values provided in the above question are as below.

x = the participants correct identified the soda = 53

n = the total number of people used in the test = 80

The sample proportion p'

p' = [tex]\frac{x}{n} = \frac{53}{80}[/tex]

p' =0.6625

The test statistic is

Z = [tex]\frac{\hat{p}-p}{\sqrt{p(1-p)/n}}[/tex]

For a large sample, we take population proportion p = 0.5

here,

Here by using an alternative hypothesis the given test is 2 tailed test.

=2*(1 - normal(Z))

=2*(1 - normal(2.91)) then press Enter we get

P-value = 0.0036

The above p-value is very small

Generally, we compare p-value with given the reject or fail to reject null hypothesis.

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