In order to make sure that their bags of chips are of sufficient weight, the Chipper Chip Company try to fill their 200 gram bags of chips with more than 203 grams. You have been given the task of investigating what proportion of bags produced do have over 203 grams of chips in them. You sample 112 bags and find that the proportion of these with over 203 grams is 0.77. You decide to construct a 95% confidence interval for the population proportion of chip bags that have more than 203 grams of chips.
a)Calculate the lower bound for this confidence interval. Give your answer as a decimal to 3 decimal places.
Lower bound for confidence interval =
b)Calculate the upper bound for this confidence interval. Give your answer as a decimal to 3 decimal places.
Upper bound for confidence interval =
A quality inspector proposes that the true proportion of chip bags with over 203 grams of chips is 0.742.
c)With a level of confidence of 95%, can/ cannot you rule out this possibility.
Need the answer...
To calculate the lower and upper bounds for the confidence interval, you can use the formula:
Lower bound = sample proportion - margin of error
Upper bound = sample proportion + margin of error
1. Calculate the margin of error:
The formula for the margin of error is:
Margin of error = z * sqrt((p(1-p))/n)
where z is the critical value, p is the sample proportion, and n is the sample size.
Since the problem doesn't provide the critical value, we can assume a 95% level of confidence, which corresponds to a z-value of 1.96 (from standard normal distribution table).
Using the given information:
Sample proportion (p) = 0.77
Sample size (n) = 112
Critical value (z) = 1.96
Calculate the margin of error:
Margin of error = 1.96 * sqrt((0.77 * (1-0.77))/112)
2. Calculate the lower and upper bounds:
Lower bound = 0.77 - margin of error
Upper bound = 0.77 + margin of error
a) Calculate the lower bound:
Lower bound = 0.77 - margin of error
b) Calculate the upper bound:
Upper bound = 0.77 + margin of error
c) To determine if the proposed proportion of 0.742 can be ruled out, check if it falls within the calculated confidence interval. You can compare the lower and upper bounds to the proposed value of 0.742.
If the proposed proportion falls within the confidence interval, then you cannot rule it out. If the proposed proportion is outside the confidence interval, then you can rule it out.
Therefore, compare the proposed proportion of 0.742 to the lower and upper bounds of the confidence interval to determine if it can be ruled out.