An environmental scientist wants to use a 95% confidence interval to estimate the mean number of hours per day her solar panel receives direct sunlight. She observed the panel for 48 randomly selected days and found that the solar panel received an average of 7.1 hours of sunlight per day and the standard deviation was 2.3 hours. Round your answers to two decimal places. A. To compute the confidence interval, use the [Select] distribution. B. With 95% confidence the population mean number of hours of sunlight the solar panel receives per day for all days is between [Select] and [Select] C. If many groups of 48 randomly selected days were observed, then a different confidence interval would be produced from each group. About [Select] percent of these confidence intervals will contain the true population mean number of hours of sunlight per day that the solar panel receives and about [Select] percent will not contain the true population mean number of hours of sunlight that the solar panel receives.

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### Estimating the Mean Number of Sunlight Hours Using a 95% Confidence Interval

An environmental scientist seeks to estimate the mean number of hours of direct sunlight her solar panel receives per day with a 95% confidence interval. The scientist observed the solar panel over a span of 48 randomly selected days, recording an average of 7.1 hours of sunlight each day. The standard deviation for the observed data was 2.3 hours.

The following steps explain how to determine the confidence interval for this data. Round your answers to two decimal places.

#### A. Determining the Correct Distribution
To compute the confidence interval, use the \([ Select ]\) distribution.

#### B. Calculating the Confidence Interval
With 95% confidence, the population mean number of hours of sunlight the solar panel receives per day is between:
\[ Select \] and \[ Select \].

#### C. Understanding Confidence Intervals
When observing many groups of 48 randomly selected days, each group will produce a different confidence interval. About \[ Select \] percent of these confidence intervals will contain the true population mean number of hours of sunlight per day that the solar panel receives, and about \[ Select \] percent will not contain the true population mean number of hours of sunlight that the solar panel receives.

Make sure to fill in the appropriate values and select the correct distributions and confidence percentages when calculating and interpreting the confidence interval data. This understanding is critical in ensuring accurate and reliable results in statistical analysis.
Transcribed Image Text:### Estimating the Mean Number of Sunlight Hours Using a 95% Confidence Interval An environmental scientist seeks to estimate the mean number of hours of direct sunlight her solar panel receives per day with a 95% confidence interval. The scientist observed the solar panel over a span of 48 randomly selected days, recording an average of 7.1 hours of sunlight each day. The standard deviation for the observed data was 2.3 hours. The following steps explain how to determine the confidence interval for this data. Round your answers to two decimal places. #### A. Determining the Correct Distribution To compute the confidence interval, use the \([ Select ]\) distribution. #### B. Calculating the Confidence Interval With 95% confidence, the population mean number of hours of sunlight the solar panel receives per day is between: \[ Select \] and \[ Select \]. #### C. Understanding Confidence Intervals When observing many groups of 48 randomly selected days, each group will produce a different confidence interval. About \[ Select \] percent of these confidence intervals will contain the true population mean number of hours of sunlight per day that the solar panel receives, and about \[ Select \] percent will not contain the true population mean number of hours of sunlight that the solar panel receives. Make sure to fill in the appropriate values and select the correct distributions and confidence percentages when calculating and interpreting the confidence interval data. This understanding is critical in ensuring accurate and reliable results in statistical analysis.
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