Questions: Current Attempt in Progress Figure 1 shows sample proportions from samples of size n=180 from a population. Estimate the value of the population parameter and estimate the standard error for the sample statistic. Figure 1 Sampling distribution Round your answers to two decimal places. p= SE=

Current Attempt in Progress Figure 1 shows sample proportions from samples of size n=180 from a population. Estimate the value of the population parameter and estimate the standard error for the sample statistic.

Figure 1 Sampling distribution Round your answers to two decimal places. p= SE=

Transcript text: Current Attempt in Progress Figure 1 shows sample proportions from samples of size $n=180$ from a population. Estimate the value of the population parameter and estimate the standard error for the sample statistic. Figure 1 Sampling distribution Round your answers to two decimal places. \[ p= \] \[ SE= \]

Solution

Solution Steps

Step 1: Identify the sample proportion (p̂)

The sample proportion (p̂) is the mean of the sampling distribution. From the histogram, the mean appears to be around 0.80.

Step 2: Calculate the standard error (SE)

The standard error (SE) of the sample proportion is calculated using the formula: \[ SE = \sqrt{\frac{p(1-p)}{n}} \] where $ p $ is the sample proportion and $ n $ is the sample size.

Given: \[ p = 0.80 \] \[ n = 180 \]

\[ SE = \sqrt{\frac{0.80 \times (1 - 0.80)}{180}} \] \[ SE = \sqrt{\frac{0.80 \times 0.20}{180}} \] \[ SE = \sqrt{\frac{0.16}{180}} \] \[ SE = \sqrt{0.0008889} \] \[ SE \approx 0.03 \]

Final Answer

\[ p = 0.80 \] \[ SE = 0.03 \]

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