In a survey of 400 college students, 40 were left-handed. Treating the sample as if it were random and using 0.015 as the standard deviation of the sampling distribution of the sample proportion, what is the lower bound of a 95% confidence interval for the population proportion?

Question

In a survey of 400 college students, 40 were left-handed. Treating the sample as if it were random and using 0.015 as the standard deviation of the sampling distribution of the sample proportion, what is the lower bound of a 95% confidence interval for the population proportion?

Answer 1

Use a proportional confidence interval formula:

CI95 = p + or - (1.96)(0.015)
...where p = x/n
Note: + or - 1.96 represents 95% confidence interval.

For p in your problem: 40/400 = .1

I let you take it from here to calculate the interval.

Answer 2

To determine the lower bound of the 95% confidence interval for the population proportion, we can use the formula:

Lower bound = sample proportion - (Z * standard error)

First, let's calculate the sample proportion:
Sample proportion (p̂) = Number of left-handed students / Total sample size
p̂ = 40 / 400 = 0.1

Next, we need to calculate the standard error:
Standard error (SE) = standard deviation / square root of sample size
SE = 0.015 / √400 = 0.015 / 20 = 0.00075

Now, let's find the Z-value corresponding to a 95% confidence level.
Since the confidence interval is two-tailed, we divide the desired confidence level (95%) by 2 to get the tail area on each side: α/2 = 0.025.
We can then find the Z-value using a standard normal distribution table or a calculator. The Z-value for a tail area of 0.025 is approximately 1.96.

Finally, we can substitute the values into the formula to find the lower bound:
Lower bound = 0.1 - (1.96 * 0.00075)
Lower bound = 0.1 - 0.00147
Lower bound ≈ 0.0985

Therefore, the lower bound of the 95% confidence interval for the population proportion is approximately 0.0985.

Answer 3

To find the lower bound of a confidence interval for a population proportion, we can use the formula:

Lower Bound = Sample Proportion - (Z-score * Standard Error)

Here, we have the following information:

Sample Proportion (p̂) = 40/400 = 0.10 (since 40 out of 400 students were left-handed)
Z-score for a 95% confidence interval = 1.96 (for a 95% confidence interval, the Z-score is approximately 1.96)
Standard Error (SE) = 0.015

Now, let's substitute these values into the formula to calculate the lower bound:

Lower Bound = 0.10 - (1.96 * 0.015)

Calculating this equation will give us the lower bound of the confidence interval.