Question

A random sample of 36 pizzas at Vinnie Gumba's Pizza Joint yields the following results for their 12 Inch Pizza:

the sample mean diameter of pizzas equals 11.5 inches

14 people out of 36 ordered the “Gumba Special”, pizza (pineapple, anchovies, and garlic)

it is known from previous studies that the sample standard deviation equals 2.0 inches.

1. What sample size is required if you want to be 90% sure that the sample mean will be within 0.1 inches of the true mean?

2. Test the hypothesis that the true population mean of a small pizza is less than 12 inches. Set the Type I error equal to 1%.

3. Test the hypothesis that the true population means of a small pizza is not equal to 12 inches. Set the Type I error equal to 10%.

Answer 1

Ans:

1)

sample size required,n=(1.645*2/0.1)^2=1082

2)

Test statistic:

z=(11.5-12)/(2/SQRT(36))

z=-1.5

p-value=P(z<-1.5)=0.0668

As,p-value>0.01,we fail to reject the null hypothesis.

There is not sufficient evidence to conclude that the true population mean of a small pizza is less than 12 inches.

3)

p-value(2 tailed)=2*P(z<-1.5)=0.1336

As,p-value>0.1,we fail to reject the null hypothesis.

There is not sufficient evidence to conclude that the true population mean of a small pizza is not equal to 12 inches.