8.9 THE VIDEO GAME SATISFACTION RATING CASE OsVideoGame The mean of the sample o
ID: 3437831 • Letter: 8
Question
8.9 THE VIDEO GAME SATISFACTION RATING CASE OsVideoGame The mean of the sample of 65 customer satisfaction ratings in Table 1.7 is 42.95. If we let u denote the mean of all possible customer satisfaction ratings for the XYZ Box video game system, and as- sume that the population standard deviation equals 2.64: a Calculate 95 percent and 99 percent confidence intervals for Au. b Using the 95 percent confidence interval, can we be 95 percent confident that wis at least 42 (recall that a very satisfied customer gives a rating of at least 42)? Explain. c Using the 99 percent confidence interval, can we be 99 percent confident that Au is at least 42? Explain. d Based on your answers to parts b and c, how convinced are you that the mean satisfaction rating is at least 42?Explanation / Answer
Note that
Lower Bound = X - z(alpha/2) * s / sqrt(n)
Upper Bound = X + z(alpha/2) * s / sqrt(n)
where
X = sample mean = 42.95
z(alpha/2) = critical z for the confidence interval = 1.959963985
s = sample standard deviation = 2.64
n = sample size = 65
Thus,
Lower bound = 42.30820646
Upper bound = 43.59179354
Thus, the confidence interval is
( 42.30820646 , 43.59179354 ) [95% confidence interval]
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Lower Bound = X - z(alpha/2) * s / sqrt(n)
Upper Bound = X + z(alpha/2) * s / sqrt(n)
where
X = sample mean = 42.95
z(alpha/2) = critical z for the confidence interval = 2.575829304
s = sample standard deviation = 2.64
n = sample size = 65
Thus,
Lower bound = 42.10654032
Upper bound = 43.79345968
Thus, the confidence interval is
( 42.10654032 , 43.79345968 ) [99% confidence interval]
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b.
Yes, because even the lower bound is higher than 42.
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c.
Also yes, because even the lower bound is higher than 42.
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d. We are convinced at 0.025 and 0.005 level; the right tails of these confidence intervals.
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