A popular consumer staple was displayed in different locations in the same aisle of a grocery store to determine what, if any, effect different placement might have on its sales. The product was placed at one of three heights on the aisle – low, medium, and high – and at one of three locations in the store – at the front of the store, at the middle of the store, and at the rear of the store. The number of units sold of the product at various height and distance combinations was recorded each week for five weeks, and the following results were obtained:
Front
Middle
Rear
Low
125
185
126
143
170
136
150
129
138
195
149
162
147
Medium
141
176
128
137
161
133
145
167
148
165
130
184
High
157
152
186
164
What effect does the product placement have on the sales?
For this you should:
i) Analyze the data with an analysis of variance. Perform all the necessary tests (including testing for treatment means, interaction and, if necessary, for main effects), and state the hypotheses and conclusions for all of them. When testing for interaction, make sure you explain precisely what interaction means in the context of this problem.
ii) Produce a profile plot of the mean number of items sold. Comment on this and relate it to your tests.
iii) Perform any relevant comparison of means procedures.
iv) State your recommendations on where the product should be placed.
Attachment: 2014-10-27_020147_negative_and_positive_z_scores.docx
1) Assume that the significance level is a = 0.05. Use the given information to find the P-value, and the critical value(s). With H₁: p ≠ , the test statistic is z = -1.75.
P-value = _______(round to four decimal places)
The critical value(s) are ____________(round to three decimal places as needed. Separate answers with commas as needed).
2) In a study of pregnant women and their ability to correctly predict the sex of their baby, 58 of the pregnant women had 12 years of education or less, and 34.5% correctly predicted the sex of their baby. Use a 0.01 significance level to test the claim that these women have no ability to predict the sex of their baby, and the results are not significantly different from those that would be expected with random guesses. Identify the null hypothesis, alternative hypothesis, test statistic, p-value, conclusion about the null hypothesis, and final conclusion that addresses the original claim. Use the P-value method. Use the normal distribution as an approximation of the binomial distribution.
A) Identify the null and alternative hypothesis
B) The test statistic is z=______(round to two decimal places)
C) The P-value is________(round to four decimal places)
D) Identify the conclusion
Fail to reject/reject? Ho is/is not?
3) Assume that the simple random sample has been selected from a normally distributed population, and test the given claim. Identify the null and alternative hypothesis, test statistic, P-value, critical value(s), and state the final conclusion that addresses the original claim.
A simple random sample of 25 filtered 100 mm cigarettes is obtained, and the tar content of each cigarette is measured. The sample has a mean of 19.2 mg and a standard deviation of 3.49 mg. Use a 0.05 significance level to test the claim that the mean tar content of 100 mm cigarettes is less than 21.1 mg which is the mean for unfiltered king size cigarettes. What do the results suggest, if anything, about the effectiveness of the filters?
A) What are the hypothesis?
B) t= _______ (round to three decimal places as needed)
C) The P-value is ______(round to four decimal places as needed)
D) The critical value(s) is/are ________(round to three decimal places as needed. Separate answers with commas as needed)
E) Fail to reject/reject Ho? There is sufficient/insufficient evidence?
F) What do the results suggest?
4) The blood pressure measurements of a single patient were taken by 12 different medical students, and the results are listed below. Construct a scatterplot, find the value of the linear correlation coefficient r, and find the P-value using a= 0.05. Is there sufficient evidence to conclude that there is a linear correlation between systolic measurements and diastolic measurements?
systolic_(x)
diastolic_(y)
135
93
92
140
99
120
81
90
122
84
83
144
97
105
139
94
A) What are the null and alternative hypothesis?
B) The linear correlation coefficient r is ______(round to three decimal places as needed)
C) The test statistic t is ______(round to three decimal places as needed)
D) Because the P-value is less/greater than the significance level 0.05, there is/is not sufficient evidence to support the claim?
5) Suppose IQ scores were obtained from randomly selected siblings. For 20 such pairs of people, the linear correlation coefficient is 0.810 and the equation of the regression line is у(this is one on top the other)= 26.7+0.74x, where x represents the IQ score of the older child. Also the 20 x values have a mean of 100.47 and the 20 y values have a mean of 101.1. What is the best predicted IQ of the younger child, given that the older child has an IQ of 99? Use a significance level of 0.05. SHOW ALL WORK
A) The best predicted IQ of the younger child is _______(round to two places as needed)
6) In a test of the effectiveness for lowering cholesterol, 49 subjects were treated with garlic in a processed tablet form. Cholesterol levels were tested before and after the treatment. The changes in their levels of LDL cholesterol (mg/dL) have a mean of 3.8 and a standard deviation of 17.5 . Complete parts A and B below. SHOW ALL WORK.
A) What is the best point estimate of the population mean net change in LDL cholesterol after the garlic treatment?
The best point estimate is _____mg/dL. (type an integer or a decimal)
B) Construct a 95% confidence interval estimate of the mean net change in LDL cholesterol after the garlic treatment. What does the confidence interval suggest about the effectiveness of garlic in reducing LDL cholesterol?
______mg/dL < µ < _____mg/dL (round to two decimal places as needed)
C) What does the confidence interval suggest about the effectiveness of the treatments?