Estimating a Population Mean

The mean score of the random sample of 49 Grade 11 students who took the first periodic test is calculated to be 78. The population variance is known to be 0.16. The confidence level is equal to 95. What is the confidence interval for the mean of the entire Grade 11 students?

The mean score of the random sample of 49 Grade 11 students who took the first periodic test is calculated to be 78. The population variance is known to be 0.16. The confidence level is equal to 95. What can you conclude about the confidence interval of the population mean?

• The researcher is 95% confident that the  is between 77.98 and 78.11           

• The researcher is 95% confident that the  is between 79.78 and 71.18           

• The researcher is 95% confident that the  is between 77.89 and 78.11  

• The researcher is 95% confident that the  is between 77.89 and 78.10                    

The mean score of the random sample of 49 Grade 11 students who took the first periodic test is calculated to be 78. The population variance is known to be 0.16. The confidence level is equal to 95.

What is the margin of error?

• 0.025

• 0.4750

• 0.112

• 77.89

What is the minimum sample size required to estimate the unknown population mean given a confidence interval of 95%, margin of error of 75 and a standard deviation of 250?

• 42.68

• 43

• 42.7

• 43.01

• 0.05

• 0.025

• 0.475

• 1.96

Imagine a researcher is interested in estimating the average height of plants in a large botanical garden. To achieve this, they decide to take samples from different sections of the garden. What is the primary reason for using the sampling distribution of the sample mean in this scenario?

• To directly measure the height of every plant in the garden

• To estimate the average height of plants in the entire garden from the sample means

• To prove that the sampled plants are taller than the rest

• To show that sampling is unnecessary in large populations

Imagine a researcher wants to understand the average time spent on social media by teenagers in a city. What is the purpose of constructing a sampling distribution in this context?

• To estimate the population parameter (average time spent on social media by all teenagers in the city) from the sample statistic (average time from the sample).

• To demonstrate that sample statistics are not useful estimators of population parameters.

• To prove that the sample mean (average time from the sample) is always equal to the population mean (average time by all teenagers in the city).

• To increase the accuracy of the population parameter estimates (average time spent on social media by all teenagers in the city) by using larger samples.

Imagine a study is conducted at a university to determine the average number of textbooks a group of engineering students reads over the course of a semester. Which of the following factors would most likely increase the precision of the sampling distribution of the sample mean?

• Decreasing the sample size

• Increasing the variability of the number of textbooks read

• Increasing the sample size

• Using a convenience sample instead of a random sample

Imagine an environmental scientist measuring the pH levels of a lake at different points to assess its acidity. They plan to use these samples to estimate the lake's overall average pH level. Which of the following would most likely result in a more accurate estimation of the population mean?

• Decreasing the number of sampling points

• Sampling only from areas near the shore

• Increasing the number of sampling points

• Sampling only at the lake's deepest points

Imagine a study is conducted to assess the average daily screen time among college students. Which of the following would most likely result in a biased estimate of the population mean?

• Using a random sample of students from multiple colleges

• Surveying only students from a single study group

• Increasing the sample size

• Ensuring the sample is representative of the entire student population