Sampling And Hypothesis Testing 1

1. In one study, the length of 20 fish of a particular species type were caught and measured. All the measurements came identical to the decimal point. Can we be 100 % confident that all fish of that species type will be of the same length?

Yes

No

The fact that all 20 fish measured in the study came out to be identical to the decimal point does not guarantee that all fish of that species type will be of the same length. It is possible that the sample of 20 fish happened to have the same length, but it does not necessarily represent the entire population of fish of that species type. To be 100% confident, a larger sample size or a complete population analysis would be required.

Explanation

The fact that all 20 fish measured in the study came out to be identical to the decimal point does not guarantee that all fish of that species type will be of the same length. It is possible that the sample of 20 fish happened to have the same length, but it does not necessarily represent the entire population of fish of that species type. To be 100% confident, a larger sample size or a complete population analysis would be required.

2. Gallup conducted a survey by calling people on thier Home Telephones to find who are they likely to vote. What can be said about this survey?

Unbiased

Biased

Can't say Anything

The survey conducted by Gallup by calling people on their home telephones to find out who they are likely to vote for is biased. This is because the survey only includes people who have home telephones, which may not be representative of the entire population. It excludes those who do not have home telephones or prefer to be contacted through other means, such as mobile phones or online surveys. As a result, the survey results may not accurately reflect the opinions and voting intentions of the entire population.

Explanation

The survey conducted by Gallup by calling people on their home telephones to find out who they are likely to vote for is biased. This is because the survey only includes people who have home telephones, which may not be representative of the entire population. It excludes those who do not have home telephones or prefer to be contacted through other means, such as mobile phones or online surveys. As a result, the survey results may not accurately reflect the opinions and voting intentions of the entire population.

3. The sample mean is 40. The sample size is 20 and sample standard deviation is 25. What is the Standard error.

5

1.25

5.59

4

The standard error is a measure of the variability of the sample mean. It is calculated by dividing the sample standard deviation by the square root of the sample size. In this case, the sample standard deviation is 25 and the sample size is 20. Therefore, the standard error is 25 / √20 = 5.59.

Explanation

The standard error is a measure of the variability of the sample mean. It is calculated by dividing the sample standard deviation by the square root of the sample size. In this case, the sample standard deviation is 25 and the sample size is 20. Therefore, the standard error is 25 / √20 = 5.59.

4. Check all that are true. Standard assumptions apply (errors are normally distributed and sample is unbiased).

Holding everything else constant, as the sample size increases, the standard error increases.

Holding everything else constant, as the sample size increases, the standard error decreases.

Holding everything else constant, as the sample size increases, the standard deviation decreases.

The less the variation in the sample, the more confident we can be that the sample mean is closer to the population mean (holding everything else constant).

As the sample size increases, the standard error decreases because a larger sample size provides more precise estimates of the population parameters. With a larger sample size, there is less sampling error and the sample mean is more likely to be closer to the population mean. Additionally, when there is less variation in the sample, it indicates that the sample mean is more representative of the population mean, which increases our confidence in the estimate.

Explanation

As the sample size increases, the standard error decreases because a larger sample size provides more precise estimates of the population parameters. With a larger sample size, there is less sampling error and the sample mean is more likely to be closer to the population mean. Additionally, when there is less variation in the sample, it indicates that the sample mean is more representative of the population mean, which increases our confidence in the estimate.

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5. The sample mean is 40. The sample size is 20 and sample standard deviation is 25. Which of the following is true?

We reject the null hypothesis that population mean is above 48 at 95% confidence level

We accept the hypothesis that the population mean is within 34 and 46

We fail to reject the hypothesis that population mean is below 46 at 95% confidence level

Based on the given information, the sample mean is 40, which is below 48. Since the sample size is 20 and the sample standard deviation is 25, we can use a t-test to determine if the population mean is significantly different from a certain value. In this case, we are testing whether the population mean is above 48 or below 46 at a 95% confidence level. Since the sample mean of 40 is below 48, we reject the null hypothesis that the population mean is above 48. However, since the sample mean of 40 is also above 46, we fail to reject the hypothesis that the population mean is below 46.

Explanation

Based on the given information, the sample mean is 40, which is below 48. Since the sample size is 20 and the sample standard deviation is 25, we can use a t-test to determine if the population mean is significantly different from a certain value. In this case, we are testing whether the population mean is above 48 or below 46 at a 95% confidence level. Since the sample mean of 40 is below 48, we reject the null hypothesis that the population mean is above 48. However, since the sample mean of 40 is also above 46, we fail to reject the hypothesis that the population mean is below 46.

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