Maths4U Original · Short practice

A random sample has \(n=20,\ \sum x=480,\ \sum x^2=11634\).

Find the sample mean.

Enter one number or fraction. Use at least six decimal places when needed; a distribution calculator may be used for probabilities.

Maths4U Original · Short practice

A random sample has \(n=21,\ \sum x=525,\ \sum x^2=13265\).

Find the sample mean.

Enter one number or fraction. Use at least six decimal places when needed; a distribution calculator may be used for probabilities.

Maths4U Original · Short practice

A random sample has \(n=21,\ \sum x=525,\ \sum x^2=13265\).

Find the unbiased estimate of population variance.

Enter one number or fraction. Use at least six decimal places when needed; a distribution calculator may be used for probabilities.

Maths4U Original · Short practice

A random sample has \(n=22,\ \sum x=572,\ \sum x^2=15040\).

Find the unbiased estimate of population variance.

Enter one number or fraction. Use at least six decimal places when needed; a distribution calculator may be used for probabilities.

Maths4U Original · Short practice

A random sample has \(n=22,\ \sum x=572,\ \sum x^2=15040\).

Find the estimated standard error of the mean.

Enter one number or fraction. Use at least six decimal places when needed; a distribution calculator may be used for probabilities.

Maths4U Original · Short practice

A random sample has \(n=23,\ \sum x=621,\ \sum x^2=16855\).

Find the estimated standard error of the mean.

Enter one number or fraction. Use at least six decimal places when needed; a distribution calculator may be used for probabilities.

Maths4U Original · Short practice

A random sample has \(n=23,\ \sum x=621,\ \sum x^2=16855\).

Find the unbiased variance estimate after every observation is multiplied by 3.

Enter one number or fraction. Use at least six decimal places when needed; a distribution calculator may be used for probabilities.

Maths4U Original · Short practice

A random sample has \(n=24,\ \sum x=672,\ \sum x^2=18931\).

Find the unbiased variance estimate after every observation is multiplied by 3.

Enter one number or fraction. Use at least six decimal places when needed; a distribution calculator may be used for probabilities.

Maths4U Original · Short practice

A normal population has known standard deviation 7. An independent random sample of size 25 has mean 49. Use a two-sided 95% confidence interval, with \(\displaystyle z=1.95996398454\).

Find the interval half-width.

Enter one number or fraction. Use at least six decimal places when needed; a distribution calculator may be used for probabilities.

Maths4U Original · Short practice

A normal population has known standard deviation 3. An independent random sample of size 36 has mean 50. Use a two-sided 95% confidence interval, with \(\displaystyle z=1.95996398454\).

Find the interval half-width.

Enter one number or fraction. Use at least six decimal places when needed; a distribution calculator may be used for probabilities.

Maths4U Original · Short practice

A normal population has known standard deviation 3. An independent random sample of size 36 has mean 50. Use a two-sided 95% confidence interval, with \(\displaystyle z=1.95996398454\).

Find the lower endpoint.

Enter one number or fraction. Use at least six decimal places when needed; a distribution calculator may be used for probabilities.

Maths4U Original · Short practice

A normal population has known standard deviation 4. An independent random sample of size 49 has mean 51. Use a two-sided 95% confidence interval, with \(\displaystyle z=1.95996398454\).

Find the lower endpoint.

Enter one number or fraction. Use at least six decimal places when needed; a distribution calculator may be used for probabilities.

Maths4U Original · Short practice

A normal population has known standard deviation 4. An independent random sample of size 49 has mean 51. Use a two-sided 95% confidence interval, with \(\displaystyle z=1.95996398454\).

Find the upper endpoint.

Enter one number or fraction. Use at least six decimal places when needed; a distribution calculator may be used for probabilities.

Maths4U Original · Short practice

A normal population has known standard deviation 5. An independent random sample of size 16 has mean 52. Use a two-sided 95% confidence interval, with \(\displaystyle z=1.95996398454\).

Find the upper endpoint.

Enter one number or fraction. Use at least six decimal places when needed; a distribution calculator may be used for probabilities.

Maths4U Original · Short practice

A normal population has known standard deviation 5. An independent random sample of size 16 has mean 52. Use a two-sided 95% confidence interval, with \(\displaystyle z=1.95996398454\).

Find the minimum sample size for half-width at most 1.2, using the same σ and confidence level.

Enter one number or fraction. Use at least six decimal places when needed; a distribution calculator may be used for probabilities.

Maths4U Original · Short practice

A normal population has known standard deviation 6. An independent random sample of size 25 has mean 53. Use a two-sided 95% confidence interval, with \(\displaystyle z=1.95996398454\).

Find the minimum sample size for half-width at most 1.25, using the same σ and confidence level.

Enter one number or fraction. Use at least six decimal places when needed; a distribution calculator may be used for probabilities.

Maths4U Original · Short practice

A random sample records 65 successes out of 220 independent trials. Use a large-sample normal 95% confidence interval, with \(\displaystyle z=1.95996398454\).

Find the estimated population proportion.

Enter one number or fraction. Use at least six decimal places when needed; a distribution calculator may be used for probabilities.

Maths4U Original · Short practice

A random sample records 68 successes out of 230 independent trials. Use a large-sample normal 95% confidence interval, with \(\displaystyle z=1.95996398454\).

Find the estimated population proportion.

Enter one number or fraction. Use at least six decimal places when needed; a distribution calculator may be used for probabilities.

Maths4U Original · Short practice

A random sample records 68 successes out of 230 independent trials. Use a large-sample normal 95% confidence interval, with \(\displaystyle z=1.95996398454\).

Find the estimated standard error.

Enter one number or fraction. Use at least six decimal places when needed; a distribution calculator may be used for probabilities.

Maths4U Original · Short practice

A random sample records 71 successes out of 240 independent trials. Use a large-sample normal 95% confidence interval, with \(\displaystyle z=1.95996398454\).

Find the estimated standard error.

Enter one number or fraction. Use at least six decimal places when needed; a distribution calculator may be used for probabilities.

Maths4U Original · Short practice

A random sample records 71 successes out of 240 independent trials. Use a large-sample normal 95% confidence interval, with \(\displaystyle z=1.95996398454\).

Find the lower confidence endpoint.

Enter one number or fraction. Use at least six decimal places when needed; a distribution calculator may be used for probabilities.

Maths4U Original · Short practice

A random sample records 74 successes out of 250 independent trials. Use a large-sample normal 95% confidence interval, with \(\displaystyle z=1.95996398454\).

Find the lower confidence endpoint.

Enter one number or fraction. Use at least six decimal places when needed; a distribution calculator may be used for probabilities.

Maths4U Original · Short practice

A random sample records 74 successes out of 250 independent trials. Use a large-sample normal 95% confidence interval, with \(\displaystyle z=1.95996398454\).

Find the interval width.

Enter one number or fraction. Use at least six decimal places when needed; a distribution calculator may be used for probabilities.

Maths4U Original · Short practice

A random sample records 77 successes out of 260 independent trials. Use a large-sample normal 95% confidence interval, with \(\displaystyle z=1.95996398454\).

Find the interval width.

Enter one number or fraction. Use at least six decimal places when needed; a distribution calculator may be used for probabilities.