Unit 7: Inference for Quantitative Data: Means

A nutritionist measures the sodium content (mg) of 20 randomly selected frozen dinners: [math] mg, [math] mg.

A car manufacturer claims its new model averages 35 mpg. A consumer group tests 25 randomly selected cars and gets [math] mpg with [math] mpg.

A researcher compares study hours between two groups of college students. Group A (morning studiers, [math]): [math] hrs/week, [math]. Group B (evening studiers, [math]): [math] hrs/week, [math].

To test a new SAT prep program, 15 students take a diagnostic test before and after the program. The mean improvement (after − before) is [math] points with [math] points.

A study compares the effectiveness of two teaching methods for reading comprehension. Method A ([math]): [math], [math]. Method B ([math]): [math], [math].

A researcher has data from 12 subjects. The dotplot of the data shows one high outlier. The sample mean is [math] and [math].

For each scenario below, identify the appropriate inference procedure and justify your choice. \nScenario 1: A school tests whether average daily screen time for its 50 randomly selected students exceeds 4 hours. Data: [math], [math]. \nScenario 2: R

A taste test compares two brands of cola. Each of 20 randomly selected participants tastes both brands (order randomized) and rates them on a 1–10 scale. Summary of differences ([math]): [math], [math].

A nutritionist wants to estimate the mean calorie intake per day for college students. She plans to collect a random sample and construct a 95% confidence interval. \nPilot study results (small sample): [math], [math], [math].\nLarger follow-up study

A city claims the mean commute time for its workers is 25 minutes. A reporter suspects it is longer. She surveys a random sample of 36 workers and finds [math] minutes, [math] minutes. Assume no extreme outliers.