The average age for licensed drivers in a county is µ= 42.6, σ= 12 and the distribution is approximately normal. A county police officer was interested in whether the average age of those receiving parking tickets in the county differed from that of the average age of the population of licensed drivers in the county. She obtained a random sample of N = 25 drivers in the county, who received parking tickets. The average age for these drivers was M= 40.5.
Identify the appropriate hypothesis for analyzing this data including the conditions for using this test.
H0: μ = 42.6
H1: μ ≠ 42.6
Conditions: The sample size is 25 and the population standard deviation is known (σ = 12).
To analyze the data and determine if there is a difference between the average age of drivers who received parking tickets and the average age of the population of licensed drivers in the county, we can use a one-sample t-test.
The appropriate hypothesis for this analysis can be stated as follows:
Null Hypothesis (H₀): The average age of drivers who received parking tickets is equal to the average age of the population of licensed drivers in the county (μ = 42.6).
Alternative Hypothesis (H₁): The average age of drivers who received parking tickets is different from the average age of the population of licensed drivers in the county (μ ≠ 42.6).
To use a one-sample t-test, the following conditions should be satisfied:
1. Random Sample: The sample of 25 drivers who received parking tickets should be randomly selected from the population of licensed drivers in the county.
2. Independence: The ages of the drivers who received parking tickets should be independent of each other.
3. Normality: The distribution of ages for licensed drivers in the county should be approximately normal. This condition can be met since it is stated that the distribution is approximately normal.
By confirming that these conditions are met, we can proceed with analyzing the data using a one-sample t-test to determine if there is a significant difference between the average age of drivers who received parking tickets and the average age of the population of licensed drivers in the county.
The appropriate hypothesis for analyzing this data is a one-sample t-test.
The null hypothesis (H0) is that there is no difference between the average age of drivers who received parking tickets and the average age of the population of licensed drivers in the county. Mathematically, this can be stated as:
H0: µ = 42.6
The alternative hypothesis (Ha) is that there is a difference between the two average ages. Mathematically, this can be stated as:
Ha: µ ≠ 42.6
The conditions for using this test are as follows:
1. Random sample: The police officer obtained a random sample of N = 25 drivers who received parking tickets.
2. Normally distributed population: The distribution of the driver's ages in the county is approximately normal.
3. Independence: Each driver in the sample should be independent of each other.
4. Sufficiently large sample size: There is no specific rule for the sample size, but a general guideline is to have at least 30 samples. In this case, the sample size is 25, which is slightly lower than the guideline, but it can still be used for the t-test as long as other assumptions are met.