For each scenario write the letter for what statistical method would be used: (m
ID: 3359220 • Letter: F
Question
For each scenario write the letter for what statistical method would be used: (match with correct letter)
A. One sample z-test for a mean
B. One sample t-test for a mean
C. Two-sample t-test for means dependent
D. Two sample t-test for means independent
E. One sample z-test for a proportion
F. Two sample z-test for p1-p2
G. None of the above
____ A traffic engineer wants to determine if the average number of cars driven on a new bridge is greater than the original traffic estimates made before the bridge was opened. Before the bridge opened, it was estimated that an average of 150,000 cars would cross the bridge each day, and it is known from prior similar bridges that the number of car crossings per day on this bridge will be normally distributed. The traffic engineer takes a random sample of 15 days, and gets a mean of 148,399 cars per day with a standard deviation of 1,512 cars per day. Test the claim that the average traffic volume is different than the original estimate.
____ A consumer products company wants to measure the difference in product satisfaction between two of its products (women’s hand lotions). A random sample of 95 women was taken who used the hand lotion Lavenderaux, and 35 women reported being satisfied. A random sample of 80 different women was taken who used the hand lotion Winter-Dream, and 28 women reported being satisfied.
____ A meteorologist wants to test to see if there is a mean difference in temperatures between two US cities, Houston and Dallas. The meteorologist takes a random sample of 45 days throughout the year, and then measures the mean temperature in Houston and Dallas on each of those days.
____ A speech language pathologist wants to know if there is a difference in means in students’ speech abilities (as measured by a standardized test) between two different schools in a major city. A sample of 40 students is taken from Four Tree Hill Elementary School (with a mean score of 81.4 points, and standard deviation of 5.9 points) and a sample of 40 students is taken from Lawson’s Creek Elementary School (with a mean score of 79.6 points, and standard deviation of 6.1 points).
Explanation / Answer
1)
One sample t test for mean , because we have been given xbar , mu and sd , also n = 15 , which is less than 40 . Hence we would go for 1 sample t test
2) Two sample z-test for p1-p2
here we are given 2 proprtion ,
p1 = 35/95
and p2 = 28/80
3)
The is Two sample t-test for means independent
Because the measurements are done foe 2 different cities , where temp recording of one city is independent of the other city
4)
Two sample t-test for means independent
Because we are selecting students froom 2 different schools
we know the standard deviations and the mean values for these 2 schools differently and hence we can perform an independent 2 samples t test to check the difference in the mean values
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