The correct notation for High Voltage, Inc. to construct its null and alternative hypotheses is:
A. H0: μ(H, volt - comp) = 0 (The mean of the differences in life spans equals 0.)
Ha: μ(H, volt - comp) ≠ 0 (The mean of the differences in life spans doesn't equal 0.)
Notations for null and alternative hypotheses
The correct notation for High Voltage, Inc. to construct its null and alternative hypotheses is:
A. H0: μ(H, volt - comp) = 0 (The mean of the differences in life spans equals 0.)
Ha: μ(H, volt - comp) ≠ 0 (The mean of the differences in life spans doesn't equal 0.)
In this case, High Voltage is interested in knowing if there is a difference in the mean life span between its product and that of a competitor.
The null hypothesis (H0) states that the mean of the differences in life spans is equal to 0, indicating no difference between the two products.
The alternative hypothesis (Ha) states that the mean of the differences in life spans is not equal to 0, indicating a significant difference between the two products. This is the appropriate hypothesis notation for testing the difference in means.
Complete question
High Voltage, Inc., a light bulb manufacturer, wants to know if there's a difference in mean life span between its product and that of a competitor. They collect paired data and calculate the difference in each pair to create one set of numbers that represents the differences within each pair. What notation should High Voltage use to construct its null and alternative hypotheses?
A. H0: mu(H, volt - comp) = 0 (The mean of the differences in life spans equals 0.)
Ha: mu(H, volt - comp) ≠ 0 (The mean of the differences in life spans doesn't equal 0.)
B. H0: mu(H, volt - comp) = 32 (The mean of the differences in life spans calculated from a sample of High Voltage bulbs equals 32.)
Ha: mu(H, volt - comp) ≠ 32 (The mean of the differences in life spans calculated from a sample of High Voltage bulbs doesn't equal 32.)
C. H0: mu(H, volt - comp) = 28 (The mean of the differences in life spans calculated from the sample of the competitor's bulbs equals 28.)
Ha: mu(H, volt - comp) ≠28 (The mean of the differences in life spans calculated from the sample of the competitor's bulbs, doesn't equal 28.)
D. H0:mu(H, volt - comp) = 35 (The mean of the differences in life spans equals 35, which is the life span in hours of its bulbs as determined in previous studies.)
Ha: mu(H, volt - comp) ≠ 35 (The mean of the differences in life spans doesn't equal 35, which is the life span in hours of its bulbs as determined in previous studies.)
E. H0: mu(H, volt - comp) = 0 (The mean of the differences in life spans equals 0.)
Ha: mu(H, volt - comp) ≠ 4 (The mean of the differences in life spans equals 4, which is the number of hours High Voltage thinks is the difference in mean life span between the two bulbs.)