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A researcher took a random sample of 100 students from a large university. She computed a 95% confidence interval to estimate the average weight of the students at this university. The confidence interval was too wide to provide a precise estimate. True or false? The researcher could produce a narrower confidence interval by increasing the sample size to 150. True False

Respuesta :

Answer:True

Explanation: increasing the sample size to 150 will reduce the width of the confidence interval because it reduces the standard error.

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fichoh

The sample size refers to the number of samples used in an experiment. When determining the confidence interval, increasing the sample size makes the value obtained close to that obtained from the population. Hence, increasing the sample size would narrow the confidence interval. TRUE.

  • Confidence interval = xbar ± z(σ/√(n))

The sample size is the value of n in the formula.

  • Sample size being the numerator, reduces the value of the standard error σ/√(n) as it is increased.

  • When the value of the standard error decreases, the confidence interval has a narrower margin

Therefore, as the sample size increases, the width of the confidence interval is narrowed.

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