MATH 1342 Elementary Statistical Methods Lab 4 Name ___________________________ A researcher was tasked with determining whether the video display used by travel agents for booking airline reservations should be in color or in black and white. Market research has shown that travel agencies were primarily concerned with the speed at which reservations can be made. Therefore, the question was whether color displays allow travel agents to book reservations faster. Fifty subjects were tested with color displays (x-bar = 503 sec, s = 9.3 sec) and fifty subjects were tested with black and white displays (x-bar = 508.2 sec, s = 9.0 sec). Test if the reservations made on the color displays were significantly faster (less time) than those made on the black and white displays at a significance level of 0.05. 1. Write the null and alternative hypothesis. 2. Would you reject the null hypothesis? Justify your answer using a complete sentence and proper grammar. Be sure to show the statistics that were used to make your decision. 3. Write out the final conclusion for this hypothesis test as you would present it to the travel agency. Use complete sentences and proper grammar. 4. The agencies, however, are not concerned with statistical significance. The agencies would like to know if the difference in speed is of practical importance to them. Market research has shown that in order to justify the higher price of color displays, they must be faster by an average of at least 10 seconds per transaction. 5. Construct a 90% confidence interval for the difference in the means (color minus black and white). 6. Use the interval to explain to the agencies if they should or should not pay for color displays. Use complete sentences and proper grammar. 7. Researchers wondered whether the size of a person's brain was related to the individual's mental capacity. They selected a sample of right-handed introductory psychology students who had SAT scores higher than 1350. The subjects took the Wechsler Adult Intelligence Scale-Revised to obtain their IQ scores. MRI scans were performed at the same facility for the subjects. The scans consisted of 18 horizontal MR images. The computer counted all pixels with a nonzero gray scale in each of the 18 images, and the total count served as an index for brain size. MRI Count 816,932 951,545 991,305 833,868 856,472 852,244 790,619 866,662 857,782 948,066 IQ 133 137 138 132 140 132 135 130 133 133 a) On the axes above, draw a scatter diagram treating MRI count as the explanatory variable and IQ as the response variable. Label the graph! b) Test whether there is a linear relationship between MRI count and IQ. c) Predict the IQ score for a subject who has an MRI count of 850,000. 8. One of the biggest factors in determining the value of a home is the square footage. The following data represent the square footage and asking price (in thousands of dollars) for a random sample of homes for sale in Naples, Florida, in December 2010. Sq. Footage 1148 1096 1142 1288 1322 1466 1344 1544 1494 Asking Price ($) 154,000 159,900 169,000 169,900 170,000 179,900 180,000 189,000 189,900 a) Draw a scatter diagram treating the square footage as the explanatory variable and asking price as the response variable. Label the graph! b) There is a linear relationship between the square footage and asking price. For each of the following, use the proper format for the monetary values. i. State the linear correlation coefficient ii. Find the least-squares regression line. iii. Predict the asking price if the square footage is 1500. iv. Would a prediction for the asking price of a home that is 3350 square feet be reasonable? Why or Why not? Use a complete sentence and proper grammar. v. Interpret the slope. Use a complete sentence and proper grammar