Confidence Intervals

2. In order to determine the average amount spent in November on Amazon.com a random sample of 144 Amazon accounts were selected. The sample mean amount spent in November was $250 with a standard deviation of $25. Assuming that the population standard deviation is unknown, what is a 95% confidence interval for the population mean amount spent on Amazon.com in November?

(2) Give that a sample of 25 had x = 75, and (x-x)² = 48 the mean and standard

Determine the minimum sample size required to construct a 95% confidence interval for the population mean.  Assume the population's standard deviation is .2 inches.

Body weight expressed as a percentage of ideal in an SRS of n = 9 girls selected at random are as follows {114, 100, 104, 94, 114, 105, 103, 105, 96}. Calculate a 95% confidence interval for the population mean µ.

Topics Distribution of the sample mean. Central Limit Theorem. Confidence intervals for a population mean. Confidence intervals for a population proportion. Sample size for a given confidence level and margin of error (proportions). Poll articles. Hypotheses tests for a mean, and differences in means (independent and paired samples). Sample size and power of a test. Type I and Type II errors. You will be given a table of normal probabilities. You may wish to be familiar with the follow formulae and their application.

If the population was distributed normally the sample size to be taken will decrease. As the population normally distributes the variance and standard deviation population means will decrease so less number of sample would be appropriate to give good estimates of disease severity to determine the disease epidemics.

6. When do the mean and median have the same value? 7. Describe the relationship between variance and standard deviation.

3. In one elementary school, 200 students are tested on the subject of Math and English. The table below shows the mean and standard deviation for each subject.

The margin of error is 2%, “that is the amount of error that the CEO finds acceptable for him” (The Importance and Effect of Sample Size) (2016). If 90% of the people that were surveyed said yes, and 10% answer no, the CEO tolerance level for error might be able to be increased the it being 50/50. The confidence level that is trying to be reached by the CEO is 95.44. The confidence level is the doubt the CEO will tolerate. Let’s say the CEO has 30 yes or no questions on his survey. Having a confidence level of 95%,

Assume 20% of all email is spam. A large Internet provider plans on conducting a survey of 900 emails to see what percentage are spam.

There are only 25 numbers in the sample collected. For purposes of analysis, it will be considered that the process itself is normally distributed, and its standard deviation is unknown. Under these conditions, the formula that gives the confidence interval is:

2.56 0.60 48.86 3.64 73.43 40.16 63.63 102.47 4.06 1.37 0.63 0.56 4.63 1.25 34.33% 11.19% 5.70% 9.98% 21.17%

Discuss the implication of your statistical findings in terms of the belief that some owners of the automobiles experienced automobile failures.

For many years the mean checking balance has been $1600. Does the sample data indicate that the mean account balance has declined from this value?

The Central Limit Theorem is a statistical theory which states that the shape of a sampling distribution is approximately normal no matter the shape of the population when graphed. This theory works as long as the sample size is larger than 30.