Q1: For each scenario write the letter for what statistical method would be used
ID: 3358859 • Letter: Q
Question
Q1: For each scenario write the letter for what statistical method would be used:
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
1.____ A young man in his 20's is shopping for an engagement ring for his fiancée. His friend tells him that the average price for an engagement ring is $10,005, but the young man doesn’t believe this. He decides to take a random sample of 40 engagement rings, and finds that the average engagement ring price is $9,779 with a standard deviation of $2,994. Find a 90% confidence interval for the true mean cost of a ring.
2.____ A neuroscience major wants to test to see if a new medicine will increase short-term memory. A random sample of 40 persons is selected to take a standardized memory test before taking the medicine, and they score an average of 6.5 points with a standard deviation of 1.3 points. The same 40 persons are then given the medicine to take for a week, and when they come back a week later to take another version of the memory test, they score an average of 7.1 points with a standard deviation of 1.6. The mean difference was 0.4 points.
3.____ In 1997, an article on Americans’ working habits concluded that the overall proportion of Americans that drank coffee before work in the morning was .46. As a coffee junkie, you believe that the proportion of all Americans who drink coffee in the work before morning has increased since then. Therefore, you take a random sample of 36 Americans and find that 18 of them, or .50, report drinking coffee in the morning before work.
4.____ A historian working as a consultant for a Hollywood World War II film wants to know if the proportion of planes built by the Allies that were shot down was different than the proportion of planes built by the Axis that were shot down. He randomly takes a sample of 200 planes from Allies production and flight records and finds that 36% were shot down, and he takes a random sample of 150 Axis planes from production and flight records and finds that 40% were shot down.
5.____ As a marketing manager for a sports drink company, you are concerned that your company’s brand, Health-E, has less brand recognition than your rival’s brand, Carbway, so, you decide to test if your brand actually has less brand recognition than your rival. Therefore, you take a random sample of 330 Americans and find that 90% of them have heard of your company’s brand, Health-E, and you take another random sample of 360 Americans and find that 96% of them have heard of your rival’s brand, Carbway.
6.____ 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.
7.____ 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.
8.____ 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.
9.____ 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).
10.____ A political scientist wants to know if the proportion of Americans that can name at least one Supreme Court justice is different than what it was in 2010, when only 35% of Americans could name at least one Supreme Court justice (findlaw.com). The political scientist takes a random sample of 200 Americans, and finds that only 33% of Americans could name at least one Supreme Court justice.
11.____ A newly engaged couple is trying to decide how much is reasonable to spend on a honeymoon. A published study cited by several wedding magazines indicated that the average honeymoon cost is normally distributed with a mean of $5,111 and standard deviation of $1,621. The couple decides that they want to spend an amount no greater than what a couple in the 75th percentile spends.
12.____ A social psychologist wants to know if there is a difference in means in the amount of jewelry pieces owned by women in two difference cities. The social psychologist takes a random sample of 150 women from Los Angeles and finds the mean number of pieces of jewelry owned to be 26.6, with a standard deviation of 7.2 pieces. The social psychologist also takes a random sample of 300 women from New York and finds the mean number of pieces of jewelry owned to be 29.0, with a standard deviation of 7.7 pieces.
13.____ An NFL owner has a decision to make about whether to re-sign his star running back, but is worried that the running back’s injury rate (i.e., proportion of games missed due to injury) is higher than the overall league rate for games missed due to injury ( .0809). A random sample of 53 professional games reveals that the running back’s proportion of games missed due to injury is .0943. Test the claim that the running back’s proportion of games missed due to injury is higher than the league proportion.
14.____ A sports enthusiast wants to know if there was a statistically significant difference between the average yards thrown per game by all NFL quarterbacks and Denver NFL quarterback John Elway during the 1980’s. It is known that the average yards thrown per game by all NFL quarterbacks in the 1980s was normally distributed with a mean of 176.4 yards and standard deviation of 46.5 yards. A sample of 7 of NFL Denver quarterback John Elway’s games revealed an average of 189.4 yards per game.
15.____ A social psychologist would like to find a 90% confidence interval for the average number of miles teenagers drive in a week. A random sample of 25 students is taken, and it’s found that their average number of miles driven per week is 75.1 miles, with a standard deviation of 20.2 miles driven.
Q2: A 95% confidence interval for the average lifetime of a cellphone was (1.89, 2.78) years.
Which of the following are statistically valid statements? (more than one statment is gonna be correct)
______ If we did 100 confidence intervals about 95 of them would capture the true average
______ 95% of confidence intervals done this way will correctly capture the true average
______ If we did many similar studies, 95% would have a sample mean between 1.89 and 2.78 years
______ 95% of the time the sample average will be within a margin of error of the true average
______ The true average lifetime of a cellphone is between 1.89 and 2.78 years with 95% confidence
______ The probability that the true average is between 1.89 and 2.78 years is either 0 or 1
______ It is completely impossible to ever actually understand what confidence really means
______ 95% of all cellphones will last between 1.89 and 2.78 years
______ We are 95% confident the average lifetime for cell phones is between 1.89 and 2.78 years
______ 95% of the time the average cell phone lifetime is between 1.89 and 2.78 years
______ There is a 95% probability the average lifetime for cellphones is between 1.89 and 2.78 years
______ The average lifetime for cellphones is between 1.89 and 2.78 years 95% of the time
______ A new confidence interval has a 95% probability of being 1.89 to 2.78 years
______ 95% of all studies would have a confidence interval between 1.89 and 2.78
______ There is a 95% probability the next confidence interval will capture the true population average
______ There is a 95% probability that the next cellphone will last between 1.89 and 2.78 years
(If could more than one expert provide and answers for these 2 questions )
Explanation / Answer
We are allowed to do 4 subparts question at a time. Post again for more subparts of question.
1)
B. One sample t-test for a mean
as population SD is not known
2)
C. Two-sample t-test for means dependent
3)
E. One sample z-test for a proportion
4)
F. Two sample z-test for p1-p2
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