Part 1 Of 1 Question 1 Of 2050 Points When Comparing Two Pop ✓ Solved

Part 1 Of 1 Question 1 Of 2050 Pointswhen Comparing Two Populati

When comparing two population means with an unknown standard deviation you use a t test and you use N-2 degrees of freedom. Pretend you want to determine whether the mean weekly sales of soup are the same when the soup is the featured item and when it is a normal item on the menu. When it is the featured item the sample mean is 66 and the population standard deviation is 3 with a sample size of 23. When it is a normal item the sample mean is 53 with a population standard deviation of 4 and a sample size of 7. Given this information we could use a t test for two independent means.

The alternative hypothesis can be proven if the alternative hypothesis is rejected. You want to determine if your widgets from machine 1 are the same as machine 2. Machine 1 has a sample mean of 50 and a population standard deviation 5 and a sample size of 100. Machine 2 has a sample mean of 52 and a population standard deviation of 6 with a sample size of 36. With an alpha of .10 can we claim that there is a difference between the output of the two machines? You want to determine if your widgets from machine 1 are the same as machine 2. Machine 1 has a sample mean of 50 and a population standard deviation 5 and a sample size of 25. Machine 2 has a sample mean of 52 and a population standard deviation of 6 with a sample size of 12. We have an alpha of .01.

You want to determine if your widgets from machine 1 are the same as machine 2. Machine 1 has a sample mean of 500 and a population standard deviation 6 and a sample size of 18. Machine 2 has a sample mean of 500.5 and a population standard deviation of 2 with a sample size of 2. With an alpha of .05 can we claim that there is a difference between the output of the two machines? You want to determine if your widgets from machine 1 are the same as machine 2. Machine 1 has a sample mean of 5 and a population standard deviation 2 and a sample size of 4. Machine 2 has a sample mean of 10 and a population standard deviation of 2 with a sample size of 64. With an alpha of .01 can we claim that there is a difference between the output of the two machines?

You want to determine if your widgets from machine 1 are the same as machine 2. Machine 1 has a sample mean of 15.1 and a population standard deviation 5 and a sample size of 12.5. Machine 2 has a sample mean of 14.9 and a population standard deviation of 6 with a sample size of 12. With an alpha of .01 can we claim that there is a difference between the output of the two machines? The null hypothesis can be proven if it is not rejected.

Pretend you are asked to test the claim that the true mean weight of gold bars in the safe is less than 15 ounces. You will have a/an. Pretend you are asked to test the claim that the true mean weight of chocolate bars manufactured in a factory is more than 3 ounces. You will have a/an. Your population mean used to be 7.1. The population standard deviation is 1.5. The sample size is 81. The sample mean is 4.2. .05 is your level of significance. The null hypothesis is that the population mean is equal to 7.1, use your sample data to test this claim. If you use this information, you will reject the null hypothesis that the population mean is equal to 7.1.

You want to determine if your widgets from machine 1 are the same as machine 2. Machine 1 has a sample mean of 24 and a population standard deviation 6 and a sample size of 12. Machine 2 has a sample mean of 18 and a population standard deviation of 6 with a sample size of 9. With an alpha of .05 can we claim that there is a difference between the output of the two machines? You want to determine if your widgets from machine 1 are the same as machine 2. Machine 1 has a sample mean of 33 and a sample standard deviation 6 and a sample size of 18. Machine 2 has a sample mean of 31 and a sample standard deviation of 6 with a sample size of 18. With an alpha of .05 can we claim that there is a difference between the output of the two machines?

You want to determine if your widgets from machine 1 are the same as machine 2. Machine 1 has a sample mean of 2,000.21 and a sample standard deviation 6.1 and a sample size of 2. Machine 2 has a sample mean of 1,998.76 and a sample standard deviation of 6.2 with a sample size of 2. With an alpha of .05 can we claim that there is a difference between the output of the two machines? A hypothesis is always a claim about a population parameter. Pretend you are asked to test the claim that the true mean size of each dump truck you fill is different from 2 tons. You will have a/an...

Your population mean used to be 6.0. The population standard deviation is 9. The sample size is 9. The sample mean is 7.0. .05 is your level of significance. The null hypothesis is that the population mean is less than or equal to 6.0, use your sample data to test this claim. If you use this information, you will reject the null hypothesis that the population mean is less than or equal to 6.0. You work at a hospital that has always had about 200 employees staffed at night. You think that the number of employees staffed at night has recently increased and would like to test this claim. If you run a hypothesis test, which of the following statements would fit your problem?

You are a manager at a firm and you believe your monthly costs have increased. The costs have always been $9,000 but you now believe they are more and would like to test this claim. If you run a hypothesis test, which of the following statements would fit your problem?

Paper For Above Instructions

In statistical analysis, comparing two population means is an essential task, especially when working with different samples and unknown parameters. This paper outlines the process of applying a t-test for the means of two independent populations and discusses various scenarios, including hypotheses, sample data, and decision-making based on statistical significance.

When faced with an unknown population standard deviation, researchers utilize the t-test, which utilizes degrees of freedom calculated as N-2, where N is the total number of observations in both samples. This is critical when analyzing comparative sales data, such as determining whether the mean weekly sales of soup differ when featured versus when a normal item. For instance, if the sample mean sales for the featured item is 66 with a standard deviation of 3 over 23 observations and the normal menu item has a mean of 53 with a standard deviation of 4 over 7 observations, a t-test can be employed.

The statistical hypothesis framework establishes two opposing statements: the null hypothesis (H0), typically representing no effect or no difference, and the alternative hypothesis (H1), which posits that a difference exists. For the soup sales example, the hypotheses can be set as follows: H0: μ_featured = μ_normal, and H1: μ_featured ≠ μ_normal.

To execute the t-test, the t statistic can be computed using the following formula:

t = (X1 - X2) / sqrt((s1^2/n1) + (s2^2/n2))

Where:

• X1 and X2 are the sample means
• s1 and s2 are the sample standard deviations
• n1 and n2 are the sample sizes

Plugging in the values, we can calculate the t-value and then compare it with the critical t-value from the t-distribution table, based on the degrees of freedom (df = N1 + N2 - 2) at a specified alpha level (commonly set at 0.05). The critical t-value helps to determine if we can reject the null hypothesis.

For each of the subsequent scenarios provided in the assignment, using a similar methodology will guide the determination of whether any significant differences exist between the population means of gadgets produced by two machines or comparing other relevant parameters.

Researchers often consider the alpha level (the threshold for rejecting the null hypothesis) while interpreting results. A common alpha level used is 0.05, though in some studies, more stringent levels like 0.01 are employed. In cases where the p-value obtained from the t-test is less than the alpha level, the null hypothesis will be rejected, indicating that the observed differences are statistically significant.

Hypothesis testing also entails making decisions based on the null hypothesis. If we withhold enough evidence to reject H0, we cannot conclude that H0 is true; we can, at best, say that we failed to find sufficient evidence against it. Hence, statistical testing does not prove hypotheses in an absolute manner but lends credence to claims based on observed data.

The analysis illustrates that it is imperative to fully articulate the population parameters, utilize appropriate statistical tests, and interpret findings carefully to substantiate claims about population means. Whether assessing cost increases for management decisions or verifying changes in employee staffing at a hospital, hypothesis testing remains a cornerstone of effective data analysis.

In summary, utilizing t-tests and understanding the hypothesis framework can enhance the reliability of the conclusions drawn from sample studies in a myriad of fields, including healthcare, manufacturing, and sales. The evidence compels us to not only observe statistical differences but to comprehend their implications in practical applications.

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