Question

Problem Set 2 Variability, Variance and Standard Deviations . Z scores and the Standard Normal Distribution • Probability and the Normal Distribution Set Version C [Please staple multiple pages together Each question is worth 1 mark unless otherwise noted. The first three questions concerns the following scenario: A researcher studying romantic attraction measures body temperature changes using a very accurate thermometer that registers temperature in degrees Kelvin (0°K = absolute zero, average human adult body temperature: u=310.0°K, O=0.4°K). 30 participants rated attractiveness of a series of photographs, and then studied the photographs of the 10 faces they rated most attractive for a later recall test. Mean body temperature for the 30 participants was M=310.8°K. To convert between Kelvin and Celsius or Fahrenheit temperature scales: • The temperature in Celsius equals the temperature in ⓇK minus 273.15 e.g., 273.15°K -273.15= 0°C e.g., 310.0°K - 273.15 = 36.85°C The temperature in Fahrenheit equals the temperature in ⓇK minus 273.15 x 9/5 +32 e.g., (273.15 °K -273.15) x 9/5 +32 = 32°F e.g., (310.0 - 273.15) x 9/5 +32 = 98.3°F 1. The research scenario does not indicate the sample standard deviation. Suppose all the temperatures were converted to Celsius. What would happen to the sample standard deviation? a. It would increase by 273.15 b. It would be multiplied by 273.15 C. It would stay the same d. It is impossible to determine without knowing the standard deviation values 2. Suppose all the temperatures were converted to Fahrenheit. What would happen the the sample standard deviation? a. It would be multiplied by 9/5+32 b. It would be multiplied by 9/5 C. It would stay the same d. It is impossible to determine without knowing the standard deviation values

Answer 1

1) option C is correct: it would stay the same (as it is linear transformation with a factor of 1)

2) option B is correct :it would be multiplied by 9/5 (for 9/5 is the multiplication factor)