You measure 49 watermelons' weights, and find they have a mean weight of 60 ounces. Assume the population standard deviation is 5 ounces. Based on this, construct a 99% confidence interval for the true population mean watermelon weight.

Give your answers as decimals, to two places

1 answer

To construct a 99% confidence interval for the true population mean watermelon weight, we can use the formula for the confidence interval based on the population standard deviation:

CI=x¯±z(σn)

Where:

  • x¯ is the sample mean.
  • z is the z-value that corresponds to the desired confidence level (99% in this case).
  • σ is the population standard deviation.
  • n is the sample size.

Step 1: Identify the values

  • Sample mean (x¯) = 60 ounces
  • Population standard deviation (σ) = 5 ounces
  • Sample size (n) = 49

Step 2: Find the z-value for 99% confidence level

For a 99% confidence level, the z-value (from the z-table) is approximately:

z2.576

Step 3: Calculate the standard error of the mean (SEM)

The standard error of the mean is calculated as follows:

SE=σn=549=570.7143

Step 4: Calculate the margin of error

The margin of error (ME) is given by:

ME=zSE=2.5760.71431.8387

Step 5: Calculate the confidence interval

Now we can calculate the confidence interval:

CI=x¯±ME=60±1.8387

Calculating the lower and upper bounds:

  • Lower bound: 601.838758.16
  • Upper bound: 60+1.838761.84

Final Result

Thus, the 99% confidence interval for the true population mean watermelon weight is:

(58.16,61.84)