Question

The manager of a local hamburger restaurant wants to study customer demand for V-Burgers, a new meatless hamburger. The salesperson for V-Burgers claims that 75% of people who normally eat hamburgers also like V-Burgers. The manager surveyed a random sample of 92 customers who have eaten V-Burgers and found that 54 of them said they would buy one again. Does this data indicate that the salesperson’s claim is too high? Use a 5% level of significance

a). State your hypotheses for the test: [4]

b). Determine the critical value or the p-value. [4]

c). From the question determine the important data with its corresponding notations. [4]

d). Calculate the test statistic for this scenario. [4]

e). Make the necessary decisions and state your conclusions. [4]

Answer 1

a).hypothesis:-

the manager's claim is the alternative hypothesis.

b).z critical value for alpha=0.05, lower tailed test be:-

p value = 0.0002 [ go to part d for explanation ]

c).given data and necessary calculations:-

sample size (n) = 92

x = number of person who would buy it again = 54

sample proportions () = x/n = 54/92 = 0.5870

population proportion (p) = 0.75

d).the test statistic for this scenario is :-

p value is :-

[ using standard normal table ]

e).decision:-

using p value approach :

p value = 0.0002 < 0.05 (alpha)

so, we reject the null hypothesis.

critical value method:

so, we reject the null hypothesis.

conclusion:-

there is sufficient evidence to claim that the salesperson’s claim is too high at 0.05 level of significance.

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