The following is a partial list of the statistical methods that we have discusse
ID: 3319004 • Letter: T
Question
The following is a partial list of the statistical methods that we have discussed: binomial, z-test, t-test, f-test, chi-square test, linear correlation, ANOVA, test of goodness of fit, test of independence, test of homogeneity, confidence interval for a mean, and none of the above
Each of the situations below can potentially be solved using one or more of the statistical methods discussed in this class. Although multiple answers may be possible, make your case for which ONE method you would use, and briefly explain why. (One or two sentences will suffice for the explanation)
Note: A listed method can be identified more than once or not at all
a) Duracell claims that the lifetime of AA battery is more than 250 hours. A consumer advocate wishes to determine whether the claim is justified. She measures the lifetimes of 24 randomly sampled AA batteries, and finds the mean to be 253 hours with a standard deviation of 4 hours.
b) A researcher wants to know whether age is related to cholesterol readings
c) The mean lifetime of all G.E. 60-watt lightbulbs is 1570 hours with a standard deviation of 130 hours. A quality compliance officer wants to know the probability that a randomly drawn sample of 100 lightbulbs will have a mean lifetime less than 1530 hours.
d) A manufacturer of tennis balls produces millions of balls each day. The balls are independently produced. The manufacturer contends that 98% of its balls conform to regulations, and have diameters between 6.54 and 6.86 centimeters. A quality control officer visits the manufacturing plant and randomly selects 12 balls. She finds two balls to be outside the specified range, and uses that information to assess whether the manufacturer has exaggerated its claims
e) A professor wants to know whether two test items, Q1 and Q2, from a test taken by 200 students were answered correctly at the same rate. Suppose 172 students answered both questions correctly, 15 students answered both questions incorrectly, 7 answered Q1 correctly and Q2 incorrectly, and 6 answered Q2 correctly and Q1 incorrectly. The professor compares the proportion of students who answered Q1 correctly against the proportion of students who answered Q2 correctly
Explanation / Answer
a) One sample - t test
EXPLANATION: Claim is that the lifetime of AA battery is more than 250 hours.
Here sample size is small and also population standard deviation is unknown. So we use student one sample 't' test
b) Linear correlation
EXPLANATION: Here both age and cholesterol readings are interrealted variables. So we used to find out the linear correlation between age and cholesterol readings.
c) One sample 'Z' test
EXPLANATION: Here the sample size is large and also population standard deviation is known. Therefore we use one sample 'Z' test
d) Confidence interval
e) Chi-square test
EXPLANATION: Here tha data is related proportions (more than 2). So we use chi-square test
Related Questions
Navigate
Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.