Statistics and Probability Exam Questions

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Question 1
The owner of a small deli is trying to decide whether to discontinue selling magazines. He suspects that only 8.2% of his customers buy a magazine and he thinks that he might be able to use the display space to sell something more profitable. Before making a final decision, he decides that for one day he will keep track of the number of customers that buy a magazine.

(a) Explain why this is a binomial experiment.

(b) Assuming his suspicion that 8.2% of his customers buy a magazine is correct, what is the probability that exactly 6 out of the first 11 customers buy a magazine? Give your answer as a decimal number rounded to two digits.

(c) What is the expected number of customers from this sample that will buy a magazine?

Question 2

Assume the competing hypotheses take the following form: H0: µ1 – µ2= 0, HA: µ1 – µ2≠ 0, where µ1 is the population mean for population 1 and µ2 is the population mean for population 2. Also assume that the populations are normally distributed and we use independent sampling. The population variances are not known and assumed to be unequal. Which of the following expressions is the appropriate test statistic?

Question 3

10.9% of the population is 65 or older. Find the probability that the following number of persons selected at random from 25 people are 65 or older.

The probability that at most 2 are 65 or older _____ (Round to three decimal places as needed.)

Question 4

You have been tasked with investigating if the mean weight of all plain milk chocolate M&Ms has decreased from the advertised weight of 0.85 grams.  To investigate, you obtain the weights of 75 randomly selected plain milk chocolate M&Ms.  Use the provided sample data and Minitab to perform a hypothesis test to test the claim that the mean weight of all plain milk chocolate M&Ms has decreased from 0.85 grams at the 0.05 significance level.  COLUMN R IS ASSIGNED THIS IS THE DATA BELOW. FOLLOWED WITH QUESTIONS TO ANSWER.

1.State the null and alternative hypotheses 

2.Attach the Minitab output containing the hypothesis test results

Using the Minitab output.

3.State the decision.  Explain your reasoning 

4.State the conclusion in terms of the scenario given above

0.804
0.852
0.901
0.741
0.887
0.727
0.923
0.938
0.795
0.710
0.861
0.783
0.664
0.890
0.962
0.833
0.827
0.862
0.577
0.867
0.783
0.770
0.831
0.855
0.859
0.759
0.900
0.738
0.790
0.540
0.987
0.915
0.860
0.757
0.855
0.953
1.027
0.947
0.775
0.889
0.808
0.918
0.831
0.817
0.810
0.774
0.671
0.697
0.812
0.732
0.962
0.902
0.820
0.844
0.801
0.962
0.750
0.885
0.724
0.872
0.777
0.829
0.853
0.659
0.960
0.776
0.867
0.787
0.880
0.814
0.884
0.907
0.792
0.735
0.994

Question 5

Discuss the implications of Type I and Type II errors: 

My null hypothesis in words is: There is no difference in the portion of people wearing a mask exiting the  Walmart in the morning compared to the evening. 

   The alternative hypothesis in words: 

     The proportion of people wearing a mask exiting the  Walmart in the morning is greater than the proportion of people wearing a mask in the evening.

Question 6

Students investigating the packaging of potato chips purchased 6 bags of Lay’s Ruffles marked with a net weight of 28.3 grams. They carefully weighed the contents of each bag, recording the following weights fin grams): 29.3, 28.2. 29.1. 28.7, 28.9, 28.5 (this gives us a mean of 28.78 grams and a standard deviation of 0.40 gams). Test appropriate hypotheses to see if the actual average weight is greater than the advertised weight on the packaging. Use a significance level of 5 percentage. 

(i) Write out the Null and Alternative Hypotheses in symbols and words. 

(ii) Using a test statistic, test the hypothesis at the 5% level of significance. 

(iii) State your conclusion using the context of the problem.

Question 7

Royal Furniture bought a sofa for $800. The sofa had a $1,400 list price. What was the trade discount rate Royal received? (Round your answer to the nearest hundredth percent.)

Question 8

The manager of a restaurant in a large city claims that waiters working in all restaurants in his city earn an average of $150 or more in tips per week. A random sample of 25 waiters selected from restaurants of this city yielded a mean of $139 in tips per week with a standard deviation of $28. Assume that the weekly tips for all waiters in this city have a normal distribution. 

a. Using the 1% significance level, can you conclude that the manager’s claim is true? Use both approaches. 

b. What is the Type I error in this exercise? Explain. What is the probability of making such  an error? 

Question 9

Jeff Richardson, the front desk clerk for a chemical distributor, is faced with the ongoing problem of receiving broken test tubes, Petri dishes, and flasks. Jeff determined some additional packaging precautions that can be taken to prevent parts breakage and has asked the director of procurement to inform suppliers of the new measures. The table gives the data for 8 suppliers in terms of the average number of pieces broken per shipment. Do the data indicate, for a significance level of 0.05, that the new measurements have decreased the average number of pieces broken?

Data

ProviderBeforeAfter
11614
21213
31812
476
5149
61915
768
81715

Question 10

An engineer has designed a valve that will regulate water pressure on an automobile engine. The valve was tested on 160160 engines and the mean pressure was 6.16.1pounds/square inches (psi). Assume the population standard deviation is 0.60.6. If the valve was designed to produce a mean pressure of 6.06.0 psi, is there sufficient evidence at the 0.050.05 level that the valve does not perform to the specifications?

Question 11

Based on a sample of 31 randomly selected years, a 90% confidence interval for the mean annual precipitation in one city is from 42.7 inches to 45.3 inches.

Find the margin of error.

Question 12

A company is trying to estimate the linear relationship between its total revenue per month (in thousands of dollars) and the number of advertisements they place on the radio every month. They have data from the past year, and it is shown in the following table.

MonthsRevenue (in $1,000s)Advertisements
Jan8.3021
Feb22.70180
Mar13.4050
Apr21.10195
May15.0096
Jun12.5044
Jul20.70171
Aug19.72135
Sep16.12120
Oct13.1075
Nov15.67106
Dec25.30198

Run a regression analysis using the Revenues as the dependent variable and the number of advertisements as the independent variable and fill in the blanks below (round to 3 spaces after decimal point):

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