A marketing expert for a pasta-making company believes that more than 40% of pas

Question

A marketing expert for a pasta-making company believes that more than 40% of pasta lovers prefer Jay's pasta. If 9 out 20 pasta lovers choose Jay's pasta over other pasta, do you agree the expert's claim at the 95% level of significance. What is the statement of this hypothesis testing? What is the value of alpha, i.e. the probability of the type one error? What is the test statistic of this hypothesis testing? What is the equation to calculate the value of this test statistic?, and what is the observed value of this test statistic in this sample? What is the critical region? For example, Z > 1.645, and what is the p value? What is your conclusion on the hypothesis testing, i.e., reject H_0 of don't reject H_0, and why? What is the scientific conclusion?

Explanation / Answer

1)

Ho: Mu >.4

Ha: Mu<=.4

2)alpha = .05

3)

t = ((9/20)-.4) / sqrt(.4*.6/20) = .456

We will use t and not Z statistic as n<30

4) Critiacal region for 95% is t> 1.729

(we get this from tdistribution table using df = n-1=19 and .05 single side )

The P-Value is .32678.

5)

Now out t statistic of .456 is < critical t value of 1.729.

We don't reject Ho as the our test statistic is not in the critical region

In other words, The result is not significant at p < .05.

6) Scientific conclusion:The marketing expert' belief that more than 40% of pasta lowers prefer Jay'pasta is right

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