Derby Leicester is a city planner preparing for a meeting with the mayor. He would like to show that the population mean age of the houses on Lincoln Street is less than the population mean age of the houses on Maple Street so that more resources are allotted to repair Maple Street. Derby uses a previous study to assume that the population standard deviation for the ages of the houses is 7.72 years for Lincoln Street and 8.39 years for Maple Street. Due to limited time, Derby randomly selects a sample of houses on Lincoln Street and the houses on Maple Street from the city’s property records and then records the age of each house in years. The results of the samples are shown in the table below. Explain whether a hypothesis test for the difference between two means of independent samples is appropriate, and if so, determine the null and alternative hypotheses for this hypothesis test, where μ1 is the population mean age of the homes on Lincoln Street and μ2 is the population mean age of the homes on Maple Street. Lincoln Street Maple Street x¯¯¯1=50.91 years x¯¯¯2=59.27 years n1=41 n2=37 Select the correct answer below: A) All of the conditions to conduct the hypothesis test are met. The null and alternative hypotheses are {H0:μ1−μ2=0Ha:μ1−μ2>0. B) All of the conditions to conduct the hypothesis test have been met. The null and alternative hypotheses are {H0:μ1−μ2=0Ha:μ1−μ2≠0. C) All of the conditions to conduct the hypothesis test are met. The null and alternative hypotheses are {H0:μ1−μ2=0Ha:μ1−μ2<0. D) Although the population standard deviations are known and the sample sizes are sufficiently large, the samples are not randomly selected and are not independent of each other. E) Although the population standard deviations are known and the samples are randomly selected and independent, the sample sizes are not sufficiently large. F) Although the samples are randomly selected, independent, and sufficiently large, the population standard deviation is not known for both neighborhoods.
Inverse Normal Distribution
The method used for finding the corresponding z-critical value in a normal distribution using the known probability is said to be an inverse normal distribution. The inverse normal distribution is a continuous probability distribution with a family of two parameters.
Mean, Median, Mode
It is a descriptive summary of a data set. It can be defined by using some of the measures. The central tendencies do not provide information regarding individual data from the dataset. However, they give a summary of the data set. The central tendency or measure of central tendency is a central or typical value for a probability distribution.
Z-Scores
A z-score is a unit of measurement used in statistics to describe the position of a raw score in terms of its distance from the mean, measured with reference to standard deviation from the mean. Z-scores are useful in statistics because they allow comparison between two scores that belong to different normal distributions.
Derby Leicester is a city planner preparing for a meeting with the mayor. He would like to show that the population
| Lincoln Street | Maple Street |
|---|---|
| x¯¯¯1=50.91 years | x¯¯¯2=59.27 years |
| n1=41 | n2=37 |
Select the correct answer below:
A) All of the conditions to conduct the hypothesis test are met. The null and alternative hypotheses are {H0:μ1−μ2=0Ha:μ1−μ2>0.
B) All of the conditions to conduct the hypothesis test have been met. The null and alternative hypotheses are {H0:μ1−μ2=0Ha:μ1−μ2≠0.
C) All of the conditions to conduct the hypothesis test are met. The null and alternative hypotheses are {H0:μ1−μ2=0Ha:μ1−μ2<0.
D) Although the population standard deviations are known and the
E) Although the population standard deviations are known and the samples are randomly selected and independent, the sample sizes are not sufficiently large.
F) Although the samples are randomly selected, independent, and sufficiently large, the population standard deviation is not known for both neighborhoods.
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