📊 statistics

1. **Problem Statement:** We want to find the sample size $n$ needed to estimate the percentage of adults gambling online with a 95% confidence level and a margin of error of 4 per

1. **State the problem**: We need to find the two z-scores symmetric about 0 that mark the middle shaded region in a standard normal distribution, where the shaded area is 0.48. 2.

1. **State the problem:** We have a poll of 511 human resource professionals where 45.8% said body piercings and tattoos are big personal grooming red flags. We need to answer part

1. **Problem Restatement:** We have overhead reach distances for adult females that are normally distributed with a mean $\mu = 200$ cm and standard deviation $\sigma = 8$ cm. We w

1. We are given a normal distribution for IQ scores with mean $\mu = 100$ and standard deviation $\sigma = 15$. 2. The problem states that the area to the right of the score $x$ is

1. The problem requires finding the standard deviation of a sample using the given values: sample size $n=302$, upper bound $U=13.8$, and lower bound $L=5.3$. 2. To proceed, we fir

1. The problem gives n = 302 (sample size), U = -13.8 (upper bound), and L = -5.3 (lower bound). 2. Assuming these bounds represent a confidence interval, the range is $$U - L = -1

1. **State the problem:** We are given the formula for the standard error or margin of error as $\sigma= \frac{2}{U-L} \times z_n$, where $U$ and $L$ are known values. 2. **Underst

1. The problem is to find the standard deviation $\sigma$ from given confidence intervals.\n2. Confidence intervals are typically given as $\bar{x} \pm z \frac{\sigma}{\sqrt{n}}$,

1. **State the problem:** We have a sample of 30 emergency room patients with an average waiting time of $174.3$ minutes and a population standard deviation of $46.5$ minutes. We w

1. **State the problem:** We want to estimate the population mean number of days it takes to sell a Chevrolet Aveo based on the sample data. We have a sample mean $\bar{x} = 54$ da

1. The problem is to find the t-value for a sample mean compared to the national average. Given: sample size $n=16$, sample mean $\bar{x}=74$, sample standard deviation $s=8$, popu

1. **Problem Statement:** Determine which of the given statements about the t statistic and standard errors are FALSE. 2. **Evaluate Each Statement:**

1. The researcher conducted a t-test resulting in $t(14) = 2.25$ with a $p$-value less than $0.05$. 2. The significance level (alpha) is $\alpha = 0.05$.

1. Let's state the problem: We want to know when a researcher should use a one-sample t-test instead of a z-test. 2. A one-sample z-test is typically used when the population mean

1. We are given a sample size $n = 15$ and the sum of squares $SS = 196$. We need to find the sample variance $s^2$ and the estimated standard error $s_m$. 2. The formula for the s

1. **State the problem:** We have a list of days absent from work for 30 workers. We need to prepare a frequency table showing how many workers have each number of absent days. 2.

1. The problem asks us to calculate the mean temperature from the following values: 12°C, 11°C, 8°C, 13°C, and 16°C. 2. To find the mean, we sum all the temperatures and then divid

1. The problem asks us to calculate the mean (average) volume of gas released from the given data. 2. The volumes given are: $32, 35, 28, 30, 30$ cm$^3$.

1. **State the problem:** Calculate the mean (average) of the values 8, 9, 7, 2, and 4. 2. **List the values:** The numbers are 8, 9, 7, 2, and 4.

1. **Problem:** For test $H_0: \mu=100$ vs $H_1: \mu>100$, sample $z=2.15$. Find the p-value. 2. This is a right-tailed test so p-value = $P(Z \geq 2.15)$.