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Bags of a certain brand of tortilla chips claim to have a net weight of 14 ounces. A representative of a consumer advocate group wishes to see if there is any evidence that the mean net weight is less than advertised and plans to construct a 95% confidence interval for the mean, using an SRS of 16 bags. Suppose he is not sure if the distribution of net weights is Normal. In which of the following circumstances would he not be safe to use a t procedure?

A. A boxplot of the data has multiple large outliers.
B. The mean and median of the data are nearly equal.
C. The sample standard deviation is large.
D. A boxplot of the data shows a very slight skew.

User Braudy
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2 Answers

6 votes

Final answer:

A t procedure might not be appropriate in situation A, where there are multiple large outliers, as they can violate the normality assumption critical for the t-distribution. Options B and D are typically not severe enough to invalidate the t procedure, and option C is unrelated to the distribution shape.

Step-by-step explanation:

The t procedure may not be appropriate when data exhibits strong violations of the assumptions underlying the t-distribution, which are that the data come from a normally distributed population and that the sample size is sufficiently large to approximate the normal distribution when the population distribution is unknown.

Among the provided circumstances, option A, where a boxplot of the data has multiple large outliers, represents a situation where the t procedure might not be safe to use. This is because large outliers can significantly affect the mean and violate the normality assumption that is critical for the t-distribution to provide reliable inference.

Option B, where the mean and median of the data are nearly equal, suggests symmetry in the distribution, indicating that the t procedure would be appropriate. Option C, a large sample standard deviation, does not necessarily disqualify the use of a t procedure, assuming the sampling distribution of the mean is approximately normal. Lastly, option D, very slight skew as shown in a boxplot, is often considered tolerable, and the t procedure may still be used if the sample size is not too small and the skewness is not severe.

User Kaliiiiiiiii
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6 votes

Answer:

A. A boxplot of the data has multiple large outliers.

D. A boxplot of the data shows a very slight skew.

Step-by-step explanation:

A) The normal distribution does not have outliers. The outliers are any point outside the 3σ interval which 99.7% of the data. The 0.3% data would not be outliers.

B) YEs the mean and median of the normal distribution are nearly equal. AS it is asymmetrical.

C) When the sample standard deviation is large the data is spread about the mean. The normal distribution is flatter and wider

D) The normal distribution is never skewed.If one end is longer then the distribution is not assymmetric and the normal distribution asymmetric meaning half is the mirror reflection of the other half.

So A and D indicate circumstances where he not be safe to use a t procedure.

User TheExit
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