In an attempt to increase business on Monday nights, a restaurant offers a free dessert with every dinner order.  Before the offer, the mean number of dinner customers on Monday was 150.  The numbers of diners on a random sample of 12 days while the offer was in effect are selected.  Can you conclude that the mean number of diners increased while the free dessert offer was in effect?

 

What is (are) the parameter(s) of interest?

 

Construct a normal probability plot and a boxplot to visualize the distribution of your sample data.  Copy and paste these graphs into your assignment.  Below the graphs, answer the following questions.

Are there any major deviations from normality?  

Are there any outliers present?  

Is it appropriate to conduct statistical inference procedures, why or why not?

 

If the answer to part iii is no, do not complete the rest of #3.

 

At the 0.05 significance level, can you conclude that the mean number of diners increased from 150 while the free dessert offer was in effect?

State the null and alternative hypotheses.

State the significance level for this problem.

Calculate the test statistic.  

Calculate the P-value and include the probability notation statement.

State whether you reject or do not reject the null hypothesis.

State your conclusion in context of the problem (i.e. interpret your results).

 

Construct a 99% confidence interval for the above data.  Interpret the confidence interval.

 

 

 According to a report of the Nielsen Company, 65% of Internet searches used Google as the search engine.  Assume that a sample of 13 searches is studied.  Let the random variable  be the number of searches where Google was used.  

 

What is the name of the probability distribution of X?  Write out the setting (i.e. write out the four requirements of a particular setting that you learned in class).

Produce a table that lists the possible values of the random variable and the corresponding probabilities of each value’s occurrence.

What is the mean of this distribution?  Show work using the formula.

What is the standard deviation of this distribution?  Show work using the formula.

Calculate the probability that of the 13 searches analyzed, at least 8 of those searches used Google.  Display a Minitab Graph with the correct portion shaded as the answer to this question.  Then, verify your answer with using the table you displayed in part (b).

 

 

According to the U.S. Department of Agriculture, 58.8% of males between 20 and 39 years old consume the minimum daily requirement of calcium.  After an aggressive “Got milk” advertising campaign, the USDA conducted a survey of 55 randomly selected males between the ages of 20 and 39 and finds that 36 of them consume the recommended daily allowance of calcium. 

 

If we conduct statistical inference above, what is (are) the parameter(s) of interest?

 

Construct a 96% confidence interval for the above data.  Interpret the confidence interval as we learned in class.  Show your work using the formulas.

 

Construct a 96% confidence interval for the above data using the Plus Four Estimate.  Interpret the confidence interval as we learned in class.  Show your work using the formulas.

At the 0.05 significance level, is there evidence to conclude that the percentage of males between the ages of 20 and 39 who consume the recommended daily allowance of calcium has increased?

State the null and alternative hypotheses.

State the significance level for this problem.

Check the conditions that allow you to use the test statistic, and, if appropriate, calculate the test statistic.

Calculate the P-value and include the probability notation statement.

State whether you reject or do not reject the null hypothesis.

State your conclusion in context of the problem (i.e. interpret your results).