Confidence Intervals

A sample of $10$ circuits from a large normal population has a mean resistance of $2$ ohms. We know from past testing that the population standard deviation is $0.3$ ohms. Calculate the $95\%$ confidence interval for the true mean resistance of population. For $95\%$ confidence interval, $z_{\frac{\alpha }{2}}=1.96$

Calculate a $98\%$ confidence interval for the population mean for the following data.

$n=32, \sum x=70.4$ and $\Sigma x^2=175.56$.

Calculate $90\%$ confidence interval for the population mean for the following data.

$n=32, \sum x=70.4$ and $\Sigma x^2=175.56$.

Calculate a $95\%$ confidence interval for the proportion of students at the college who use facebook app.At a college, a random sample of $250$ students is asked if they use a facebook app. Of the students in the sample, $92$ use this facebook.

A random sample of $120$ pairs of shoes produced at a factory finds that $24$ pairs are sub-standard. Calculate the $90\%$ confidence intervals for the proportion of shoes produced that are sub-standard.

A tree consists of hundreds of apples. $46$ apples are randomly chosen. The mean and standard deviation of this instance is found to be $86$ and $6.2$ respectively. Then find the confidence interval ?

A tree consists of hundreds of apples. 46 apples are randomly chosen. The mean and standard deviation of this instance is found to be 86 and 6.2 respectively. Determine whether the apples are big enough or not.

A sample of $11$ circuits from a large normal population has a mean resistance of $2.20$ ohms. We know from past testing that the population standard deviation is $0.35$ ohms. Calculate the $95\%$ confidence interval for the true mean resistance of population. For $95\%$ confidence interval, $z_{\frac{\alpha }{2}}=1.96$

A four-sided spinner has sides coloured red, yellow, green and blue. The probability that the spinner lands on yellow is $p$. In an experiment, the spinner lands on yellow $18$ times out of $80$ spins. Calculate an approximate $99\%$ confidence interval for the value of $p$.

A quality control check of a random sample of $120$ pairs of jeans produced at a factory finds that $24$ pairs are sub-standard. Find a $98\%$ confidence interval, calculate the following confidence intervals for the proportion of jeans produced that are sub-standard:

An $\alpha \%$ confidence interval for the population mean, based on this sample, is found to have width of $0.118 \mathrm{kg}$. Find $\alpha$ for the following data summarise the masses, $x \mathrm{kg}$, of $60$ bags of dry pet food.

$\sum x=117$ and $\sum x^2=232.72$

The worldwide proportion of left-handed people is $10\%$.

In town $B$, there is a greater proportion of left-handed people than there is in town $A$. From a random sample of $100$ people in town $B$, an $\alpha \%$ confidence interval for the proportion, $p$, of left-handed people is calculated to be $\left(0.113, 0.207\right)$.

Calculate the value of $\alpha$.

The worldwide proportion of left-handed people is $10\%$.

Find a $95\%$ confidence interval for the proportion of left-handed people in a random sample of $200$ people from town $A$.

In town $B$, there is a greater proportion of left-handed people than there is in town $A$. From a random sample of $100$ people in town $B$, an $\alpha \%$ confidence interval for the proportion, $p$, of left-handed people is calculated to be $\left(0.113, 0.207\right)$.

Show that the proportion of left-handed people in the sample from town $B$ is $16\%$.

The worldwide proportion of left-handed people is $10\%$.

Find a $95\%$ confidence interval for the proportion of left-handed people in a random sample of $200$ people from town $A$.

A random sample of $200$ bees from a colony is tested to find out how many are infected with Varroa mites. Forty bees are found to be infected.

Calculate a $99\%$ confidence interval for the proportion of the colony infected with Varroa mites.

The colony of bees will collapse and will not survive if $35\%$ or more are infected with Varroa mites. Show why it is possible, at the $99\%$ confidence level, that the colony of bees might collapse.

A random sample of $200$ bees from a colony is tested to find out how many are infected with Varroa mites. Forty bees are found to be infected.

Calculate a $99\%$ confidence interval for the proportion of the colony infected with Varroa mites.

The proportion of European men who are red-green colour-blind is $8\%$. How large a sample would need to be selected to be $95\%$ certain that it contains at least this proportion of red-green colour-blind men?

A biased coin flipped $500$ times results in tails $272$ times.

Find a $90\%$ confidence interval for the probability of obtaining a tail.

This experiment is carried out ten times. How many of the confidence intervals would be expected to contain the population proportion of obtaining a tail?

A biased coin flipped $500$ times results in tails $272$ times.

Find a $90\%$ confidence interval for the probability of obtaining a tail.

A four-sided spinner has sides coloured red, yellow, green and blue. The probability that the spinner lands on yellow is $p$. In an experiment, the spinner lands on yellow $18$ times out of $80$ spins. Find an approximate $99\%$ confidence interval for the value of $p$.