math test

If the average sales price of your 16 sold products is 20€ with a standard deviation of 2€, which is the appropriate 95% confidence interval for the population mean product sales price? Assume normality. to.25(15) - 2.131. Select one: [18.93: 21.07] [19.97; 20.05] [17.38; 22.62] [19.12; 20.88]

Confidence Interval = sample mean ± (critical value * standard error) The critical value for a 95% confidence interval when assuming normality is approximately 1.96. However, since the sample size is small (n = 16), we should use the t-distribution and the corresponding critical value. The formula for the standard error is: Standard Error = sample standard deviation / √(sample size) Given that the average sales price is 20€ with a standard deviation of 2€ and a sample size of 16, we can calculate the standard error as: Standard Error = 2 / √16 = 2 / 4 = 0.5 Confidence Interval = 20 ± (critical value * 0.5) The critical value for a 95% confidence interval with 15 degrees of freedom (n-1) is approximately 2.131 (assuming a two-tailed test). Therefore, the appropriate 95% confidence interval for the population mean product sales price is: Confidence Interval = 20 ± (2.131 * 0.5) = [19.07, 20.93] Among the given options, the closest interval to the calculated interval is: [19.12; 20.88] So, the correct answer is: [19.12; 20.88]

In a regression analysis if SSE = 150 and SSR - 50, then the coefficient of determination is Select one: 0.75 0.667 1 0.25

The coefficient of determination, denoted as R-squared (R²), is a measure of the proportion of the total variation in the dependent variable that is explained by the regression model. It is calculated as the ratio of the sum of squares explained (SSR) to the total sum of squares (SST). The coefficient of determination (R²) can be expressed as: R² = SSR / SST Given that SSR = 50 and SSE = 150, we can calculate the total sum of squares (SST) by adding SSR and SSE: SST = SSR + SSE = 50 + 150 = 200 Now we can calculate the coefficient of determination (R²) using the formula: R² = SSR / SST = 50 / 200 = 0.25 Therefore, the coefficient of determination is 0.25. Among the given options, the correct answer is: 0.25

A sample consists of four observations: {2, 8, 2, 4}. Calculate the mean, variance, mode, median and range. Show your calculations.

To calculate the mean, variance, mode, median, and range for the given sample {2, 8, 2, 4}, we can follow these steps: Mean: The mean is calculated by summing all the values in the sample and dividing by the number of observations. Mean = (2 + 8 + 2 + 4) / 4 = 16 / 4 = 4 Variance: The variance measures the spread of the data points around the mean. It is calculated as the average of the squared differences between each observation and the mean. Variance = [(2 - 4)^2 + (8 - 4)^2 + (2 - 4)^2 + (4 - 4)^2] / 4 = (4 + 16 + 4 + 0) / 4 = 24 / 4 = 6 Mode: The mode is the value(s) that appear most frequently in the sample. In the given sample, the mode is 2 because it appears twice, which is more than any other value. Median: The median is the middle value when the observations are arranged in ascending order. If there is an even number of observations, the median is the average of the two middle values. First, let's arrange the sample in ascending order: {2, 2, 4, 8} Since there are four observations, the median is the average of the two middle values: (2 + 4) / 2 = 6 / 2 = 3 Range: The range is the difference between the maximum and minimum values in the sample. Range = maximum value - minimum value = 8 - 2 = 6 Summary of calculations: Mean: 4 Variance: 6 Mode: 2 Median: 3 Range: 6

a sample of data has mean 15 and standard deviation 3, then its coefficient of variation IS: Select one: 500% 0.2% 20% 5%

The coefficient of variation (CV) is a relative measure of variability and is calculated as the ratio of the standard deviation to the mean, expressed as a percentage. To find the coefficient of variation, we divide the standard deviation by the mean and multiply by 100: CV = (Standard Deviation / Mean) * 100 Given that the sample has a mean of 15 and a standard deviation of 3, we can calculate the coefficient of variation as: CV = (3 / 15) * 100 = 0.2 * 100 = 20% Therefore, the coefficient of variation for this sample is 20%.

If mean = 25 and standard deviation is 5, then coeficient of variation is 100% 20% 40% None of these

The coefficient of variation (CV) is calculated as the ratio of the standard deviation to the mean, expressed as a percentage. To find the coefficient of variation, we divide the standard deviation by the mean and multiply by 100: CV = (Standard Deviation / Mean) * 100 Given that the mean is 25 and the standard deviation is 5, we can calculate the coefficient of variation as: CV = (5 / 25) * 100 = 0.2 * 100 = 20% Therefore, the coefficient of variation is 20%. Among the given options, the correct answer is: 20%

Type I error occurs when the null hypothesis is rejected when the null hypothesis is true.

Type II error occurs when the null hypothesis is not rejected when the null hypothesis is false.

Which of the following correlation coefficient values indicates the strongest linear relationship bets variables? 0.73 -0.78 -0.52 0

The correlation coefficient measures the strength and direction of the linear relationship between two variables. Its value ranges between -1 and 1. Among the given options, the correlation coefficient value that indicates the strongest linear relationship between variables is: • 0.73 The closer the absolute value of the correlation coefficient is to 1, the stronger the linear relationship. Therefore, a correlation coefficient of 0.73 suggests a relatively strong positive linear relationship between the variables being analyzed.

A numerical measure that describes a specific characteristic of a population is known as parameter population statistic sample

parameter

In hypothesis testing, the significance level is the: same as the confidence level probability of Type il error probability of Type l error same as the o-value

probability of Type I error.

A point estimator Ө of the population parameter Ө is unbiased if

A point estimator of the population parameter is unbiased if its expected value is equal to the true value of the population parameter. In other words, an unbiased estimator on average gives an estimate that is equal to the parameter being estimated. To provide a more general statement: A point estimator "@ " of a population parameter "θ" is unbiased if and only if: E(Ө) = θ This means that the average value of the estimator, obtained by taking repeated samples, will be equal to the true population parameter. In summary, an unbiased estimator is one that, on average, provides estimates that are equal to the true value of the population parameter.

The correct matching of the sampling techniques with their descriptions is as follows:

The population is divided into subgroups, which are randomly selected to be included in the study. Stratified The selection of independent simple random samples from each subgroup of the population. Cluster Each element of the population has an equal chance (probability) of being selected. Simple random Elements are selected at regular intervals from the sampling frame. Systematic

The following data was observed from the sample: n = 25,× = 26,5 - 10. Compute the test statistic t for the hypothesis [Hy: # > 22. What is your decision: reject or do not reject the null hypothesis? Let a - 0.05. to.05(24) - 1.711. Select one: t = -2, do not reject the null hypothesis t = 2, reject the null hypothesis + = - 2, reject the null hypothesis t = 2, do not reject the null hypothesis

To compute the test statistic t for the given hypothesis, we can use the formula: t = (x - μ) / (s / √n) where: x is the sample mean, μ is the population mean under the null hypothesis, s is the sample standard deviation, and n is the sample size. Given: n = 25 x = 26.5 μ = 22 We also have the value of the test statistic critical value at a significance level of 0.05 for a two-tailed test with 24 degrees of freedom, which is -1.711. Now, let's calculate the test statistic t: t = (x - μ) / (s / √n) = (26.5 - 22) / (10 / √25) = 4.5 / (10 / 5) = 4.5 / 2 = 2.25 Since the test statistic t (2.25) is greater than the critical value (-1.711) in absolute value, we reject the null hypothesis. Therefore, the correct answer is: t = 2, reject the null hypothesis.

A distribution that is skewed to the left (negative skew) has a mode of 17 and a median of 13. Which of the following possible value for the mean? 16 20 10 12

To determine the possible value for the mean of a left-skewed (negative-skewed) distribution with a mode of 17 and a median of 13, we can make use of the relationship between the mean, median, and mode. In a left-skewed distribution, the mode is the highest peak, the median is in between the mode and the tail, and the mean is pulled towards the tail. Since the mode is given as 17 and the median is 13, we know that the mean will be less than both of these values because of the negative skew. Among the given options, the only value that satisfies this condition is: 10