Answer:
<em>-A 90% confidence interval would be narrower than the 95% confidence interval if we don't need to be as sure about our estimate. </em>
<em>-This confidence interval is not valid since the distribution of spending in the sample data is right skewed.</em>
<em>-The margin of error is $4.4.</em>
<em>-This confidence interval is valid since the sampling distribution of sample mean would be approximately normal with sample size of 436.</em>
<em>-We are 95% confident that the average spending of all American adults over this holiday season is between $80.31 and $89.11.</em>
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Step-by-step explanation:
<em>A 90% confidence interval would be narrower than the 95% confidence interval if we don't need to be as sure about our estimate. </em>
TRUE. The 90% confidence is less strict in its probability of having the mean within the interval, so it is narrower than the 95% CI. It relies more in the information given by the sample.
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<em>In order to decrease the margin of error of a 95% confidence interval to a third of what is is now, we would need to use a sample 3 times larger. </em>
FALSE. The margin of error is z*σ/(n^0.5). So to reduce it by two thirds, the sample size n needs to be 3^2=9 times larger.
<em>This confidence interval is not valid since the distribution of spending in the sample data is right skewed.</em>
FALSE. There is no information about the skewness in the sample.
<em>The margin of error is $4.4.</em>
TRUE. The margin of error is (89.11-80.31)/2=$4.4.
<em>We are 95% confident that the average spending of these 435 American adults over this holiday season is between $80.31 and $89.11.</em>
FALSE. The CI is related to the populations mean. We are 95% confident that the average spending of the population is between $80.31 and $89.11.
<em>This confidence interval is valid since the sampling distribution of sample mean would be approximately normal with sample size of 436.</em>
TRUE. This happens accordingly to the Central Limit Theorem.
<em>95% of random samples have a sample mean between $80.31 and $89.11.</em>
FALSE. The confidence interval refers to the population mean.
<em>We are 95% confident that the average spending of all American adults over this holiday season is between $80.31 and $89.11.</em>
TRUE. This is the conclusion that is looked for when constructing a confidence interval.
