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

Question

A expert for a pasta-making company believes that more than 40% of pasta lovers marketing prefer Jay's pasta. If9 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 statements of this hypothesis testing? What is the value of a, 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. Hypothesis statement is H0:p0=0.40 vs H1: p0>0.40

2. Alpha =1-0.95=0.05

3.test statistic is z=phat-p0/sqrt(p0(1-p0)/n)=0.4564

4. Now p value is 0.3266

5. As p value is greater than alpha we accept H0

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