Question

1. In the past, the average guest check at a local restaurant was $19.35 After the menu has been redesigned, a random sample of 20 guest checks was taken, the sample mean was $17.85 with the sample standard deviation of $3.88. Assume that the guest check amounts are approximately normally distributed. Is this enough evidence to believe that the average guest check has decreased? Use

A. )A=0.10 Hypotheses:

B.)Test Statistic:

C.)Analyze data (assuming H0 is true):

D.)State a Conclusion:

2. A newspaper publisher is considering launching a new "national" newspaper in Anytown. It is known that the newspaper would have to attract over 12% of all newspaper readers in order to be successful and not go out of business. During the planning stages of this newspaper, a market survey was conducted of a sample of 400 readers. After providing a brief description of the proposed newspaper, one question asked if the survey participant would subscribe to the newspaper at its planned cost of $20 per month. Suppose that 58 participants said they would subscribe.

A) Can the publisher conclude that the proposed newspaper will be financially viable? Perform the appropriate test at a 1% level of significance.

Hypotheses:

Test Statistic:

Analyze data (assuming H0 is true):

State a Conclusion:

b) Suppose the actual value of the overall proportion of readers who would subscribe to this newspaper is 0.13. Was the decision made in part (a) correct? If not, what type of error was made?

c) Describe what a Type I and a Type II error would mean for the business and what the consequences of making each type of error would be in the context of this scenario. (use words in your explanation, no symbols)

d) The publisher decided to run the above hypothesis test at a 1% level of significance. Recall that A represents the maximum probability of making a Type I error. Write a paragraph to explain why the publisher might choose to run the test at a this level of significance instead of a higher value of A. (It may be helpful to think about the relationship between A and B & the descriptions of the types of errors from part (c)

Answer 1

1)

Answer)

A)

Null hypothesis Ho : u = 19.35

Alternate hypothesis Ha : u < 19.35

B)

Test statistics t = (sample mean - claimed mean)/(s.d/√n)

t = (17.85 - 19.35)/(3.88/√20) = -1.729

C)

As the population s.d is unknown here and we are given with sample s.d as the best estimate we will use t distribution table to estimate the p-value.

Degrees of freedom is = n-1 = 19.

For 19 dof and -1.729 test statistics, P-value from t distribution is = 0.05.

Since obtained p-value is not less than 0.05.

We fail.to reject the null hypothesis Ho.

D)

We do not have enough evidence to conclude that the average guest check has decreased.