It\'s an IE question A marketing expert for a pasta-making company believes that

Question

It's an IE 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

Solution1:

its about hypothesis testing on proportion

p is population proportion

Null hypothesis:

Ho:p=0.40

Alternative Hypothesis

H1: p>0.40

Alternative Hypothesis is the claim

Solution2:

level of significance=alpha=1-confidence level

=1-0.95

=0.05

Solution3:

z statistic

p^=sample proportion=x/n=sucesses/sample size=9/20=0.45

n= sample size=20

z=0.45-0.40/sqrt(04(1-0.4)/20]

z=0.456

z obs=0.456

Solution4:

z critical=1.96 for 95% confidence level

here z obs =0.456

z obs <Z critical

Fail to reject Null hypothesis

Accept Null hypothesis

The P-Value is 0.324195.

The result is not significant at p < 0.05.

Solution5:

Do not reject Ho

As p value >0.05 and z obs < z critical

SSolution6:

There is no sufficient evidence at 5% level of significance to support the cliam that more than 40% pasta lovers prefer Jays Pasta.

Related Questions

Navigate

• Browse (All)
• Browse I
• Subjects

---

---

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.