You measure 34 turtles' weights, and find they have a mean weight of 66 ounces. Assume the population standard deviation is 9.3 ounces. Based on this, construct a 90% confidence interval for the true population mean turtle weight.

Give your answers as decimals, to two places

To construct a confidence interval, we can use the formula:

Confidence Interval = Mean ± (Critical Value * Standard Error)

First, let's find the critical value. Since we are constructing a 90% confidence interval, we need to find the z-score associated with a confidence level of 90%. The critical value can be found using a Z-table or calculator.

For a 90% confidence level, the two-tailed critical value is approximately 1.645.

Next, let's find the standard error, which is calculated using the formula:

Standard Error = Population Standard Deviation / √Sample Size

In this case, the population standard deviation is 9.3 ounces, and the sample size is 34 turtles.

Standard Error = 9.3 / √34

Now, we can substitute the values into the confidence interval formula to calculate the confidence interval.

Confidence Interval = 66 ± (1.645 * (9.3 / √34))

Calculating the expression inside the parentheses first:

9.3 / √34 ≈ 1.6 (rounded to one decimal place)

Substituting the values into the confidence interval formula:

Confidence Interval = 66 ± (1.645 * 1.6)

Now, let's calculate the upper and lower bounds of the confidence interval.

Upper Bound = 66 + (1.645 * 1.6) ≈ 68.64 (rounded to two decimal places)

Lower Bound = 66 - (1.645 * 1.6) ≈ 63.36 (rounded to two decimal places)

Therefore, the 90% confidence interval for the true population mean turtle weight is approximately 63.36 to 68.64 ounces.

To construct a confidence interval for the true population mean turtle weight, we can use the formula:

Confidence interval = sample mean ± (Z * (population standard deviation / √n))

Where:
- Confidence interval is the range within which the true population mean is likely to fall.
- Sample mean is the mean weight of the turtles in our sample.
- Z is the critical z-value corresponding to the desired level of confidence.
- Population standard deviation is the known standard deviation of the population.
- n is the sample size.

In this case, we have the following information:
- Sample mean (x̄) = 66 ounces
- Population standard deviation (σ) = 9.3 ounces
- Sample size (n) = 34

To find the critical z-value for a 90% confidence level, we look it up in the standard normal table or use a statistical calculator. For a one-tailed test, the critical z-value is approximately 1.645.

Now, let's calculate the confidence interval:

Confidence interval = 66 ± (1.645 * (9.3 / √34))

To find the square root of 34 (√34), we can use a calculator or approximation:

√34 ≈ 5.83

Now, plug in the values:

Confidence interval = 66 ± (1.645 * (9.3 / 5.83))

Calculating the expression inside the parentheses:

9.3 / 5.83 ≈ 1.59

Confidence interval = 66 ± (1.645 * 1.59)

Calculating the expression inside the parentheses:

1.645 * 1.59 ≈ 2.61

Finally, calculate the confidence interval:

Confidence interval = 66 ± 2.61

Lower bound of the confidence interval = 66 - 2.61 ≈ 63.39
Upper bound of the confidence interval = 66 + 2.61 ≈ 68.61

Therefore, the 90% confidence interval for the true population mean turtle weight is approximately 63.39 ounces to 68.61 ounces.

90% = mean ± 2.035 SD

2.035 was found by finding table in the back of a statistics text labeled something like "areas under normal distribution" to find the proportion (.45) between score and mean to get the Z score (value in terms of standard deviation).