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A population has mean μ = 50 and standard deviation σ = 10. If all possible samples of size n = 25 are drawn from this population, what is the standard error of the sampling distribution of the mean?

A factory produces light bulbs with a mean lifespan of 1200 hours and standard deviation of 100 hours. If a random sample of 50 bulbs is selected, what is the probability that the sample mean exceeds 1220 hours?

In a population where 40% favor a new policy, what is the probability that in a sample of 200 people, the proportion favoring the policy is between 0.35 and 0.45?

A biased coin has P(heads) = 0.4. In 500 tosses, what is the probability that the number of heads is between 190 and 210?

For a t-distribution with 15 degrees of freedom, what is the probability that t is less than -2.131?

A sample of 25 measurements from a normal population yields x̄ = 48.2 and s = 3.1. What is the 95% confidence interval for the population mean?

If the population standard deviation is unknown and sample size is 18, which distribution should be used for inference about the population mean?

A population has proportion P = 0.3. What sample size is needed to ensure the standard error of the sample proportion is less than 0.02?

The Central Limit Theorem states that the sampling distribution of the mean approaches normality as:

A random sample of 16 values from a normal population has mean 42.5 and standard deviation 3.8. What is the probability that the population mean is less than 41?

In a population where 60% are Democrats, what is the probability that in a sample of 150 people, more than 100 are Democrats?

For a t-distribution with 10 degrees of freedom, what is the variance?

A quality control inspector samples 36 items from a production line. The population standard deviation is known to be 0.8 mm. What is the probability that the sample mean differs from the population mean by more than 0.2 mm?

When sampling without replacement from a finite population, the standard error is:

A sample of 20 observations from a normal population has mean 65.4 and standard deviation 4.3. What is the 99% confidence interval for the population mean?

The finite population correction factor is used when:

A population has mean 85 and variance 64. If samples of size 36 are drawn, what is the probability that the sample mean is between 83 and 87?

For a t-distribution with 25 degrees of freedom, P(t > 1.708) is approximately:

A random sample of 100 students has mean IQ score of 108 with standard deviation 15. What is the probability that the population mean IQ is greater than 105?

In a binomial experiment with n=400 and p=0.2, the sampling distribution of the proportion can be approximated by a normal distribution because:

A sample of 12 observations from a normal population has mean 24.6 and variance 6.25. What is the standard error of the mean?

The t-distribution has heavier tails than the normal distribution, which means:

A population of 1000 items has mean 50 and standard deviation 5. If a sample of 100 items is drawn without replacement, what is the standard error of the mean?

For a sample of size 40 from a normal population with unknown variance, the sampling distribution of the mean follows:

A political poll shows 220 out of 500 voters support a candidate. What is the standard error of the sample proportion?

As degrees of freedom increase, the t-distribution:

A machine fills bottles with mean 500ml and standard deviation 2ml. If 25 bottles are sampled, what is the probability that the sample mean is less than 499ml?

The Central Limit Theorem applies to:

A sample of 18 measurements has mean 32.4 and standard deviation 2.8. What is the 90% confidence interval for the population mean?

In hypothesis testing, when the population standard deviation is unknown and sample size is small, we use the t-distribution because:

A population has proportion 0.35. What is the probability that in a sample of 200, the sample proportion is within 0.03 of the population proportion?

For a t-distribution with 8 degrees of freedom, what is P(t < 2.306)?

The standard error of the mean decreases when:

A sample of 22 observations has mean 45.3 and standard deviation 4.1. What is the test statistic for testing H₀: μ = 43?

The finite population correction factor is closest to 1 when:

A manufacturer claims their batteries last 100 hours on average. A sample of 16 batteries has mean 97 hours and standard deviation 6 hours. What is the probability of obtaining such a sample if the claim is true?

The sampling distribution of the proportion is approximately normal when:

A population has mean 75 and standard deviation 8. What sample size is needed so that the standard error is 1?

For a t-distribution with 20 degrees of freedom, what is the value of t such that P(-t < T < t) = 0.90?

A sample of 30 observations from a non-normal population has mean 42 and standard deviation 5.2. The sampling distribution of the mean is:

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