Question

1. a company wants to estimate the average weight of apples in a shipment. to do so, they randomly select a sample of 25 apples and find that the sample mean weight is 6 ounces. using statkey, they calculate the approximate standard error to be 0.5 ounces.

a)state the parameter being estimatedin words and use the correct symbol.
b)state the statistic that gives the best estimatenumber and symbol.
c)give a 95% confidence interval for the quantity being estimated.

Explanation:

Step1: Identify the parameter

The parameter is the population - mean weight of apples in the shipment, denoted as $\mu$.

Step2: Identify the best - estimate statistic

The sample mean is the best estimate of the population mean. Here, the sample mean $\bar{x}=6$ ounces.

Step3: Calculate the 95% confidence interval

For a 95% confidence interval, the critical value $z$ (for a large - enough sample or known standard deviation situation, which is applicable here in the context of standard error) is approximately $z = 1.96$. The formula for the confidence interval is $\bar{x}\pm z\times SE$, where $\bar{x}$ is the sample mean, $z$ is the critical value, and $SE$ is the standard error. Substituting the values: $\bar{x}=6$, $z = 1.96$, and $SE = 0.5$.
Lower limit: $6-1.96\times0.5=6 - 0.98 = 5.02$ ounces.
Upper limit: $6 + 1.96\times0.5=6+0.98 = 6.98$ ounces.

Answer:

a) The parameter being estimated is the population - mean weight of apples in the shipment, denoted as $\mu$.
b) The statistic that gives the best estimate is the sample mean $\bar{x}=6$ ounces.
c) The 95% confidence interval is $(5.02,6.98)$ ounces.