Suppose you are conducting a survey to investigate cholesterol levels of people

Question

Suppose you are conducting a survey to investigate cholesterol levels of people living in Riverside, CA. Using this scenario, write an essay that explores the following issues(You may include equations if necessary). How would you collect the survey data? (Make sure you justify your procedure using relevant statistical theory and concepts) How would you apply the hypothesis test for one population mean to this case? How would you prove that the mean value of cholesterol levels in Riverside, CA is not equal to 210? You should provide null and alternative hypotheses statements for this particular situation. Also, discuss whether you would use z or t statistics, and why. Finally, discuss under what circumstance you would reject or accept the null hypothesis. What is the statistical rationale for rejecting or failing to rejecting the null hypothesis in this case? Your justification should be based on the comparison of p-value and significance level. Note that this is a hypothetical scenario, and you can make up numbers, but your arguments should be based on appropriate statistical concepts and theory

Explanation / Answer

Solution:-

a) Survey researchers employ a variety of techniques in the collection of survey data. People can be contacted and surveyed using several different modes: by an interviewer in-person or on the telephone (either a landline or cellphone), via the internet or by paper questionnaires (delivered in person or in the mail).

In this case we can go for simple random

A simple random sample is a subset of a statistical population in which each member of the subset has an equal probability of being chosen.

b)

We will find the mean and standard deviation of the chossen sample.

We will do one-sample t-test. The test will be two tailed test.

c)

State the hypotheses. The first step is to state the null hypothesis and an alternative hypothesis.

Null hypothesis: = 210

Alternative hypothesis: 210

Note that these hypotheses constitute a two-tailed test. The null hypothesis will be rejected if the sample mean is too big or if it is too small.

Formulate an analysis plan. For this analysis, the significance level is 0.05. The test method is a one-sample t-test.

Analyze sample data. Using sample data, we compute the standard error (SE), degrees of freedom (DF), and the t statistic test statistic (t).

SE = s / sqrt(n)

DF = n - 1

t = (x - ) / SE

where s is the standard deviation of the sample, x is the sample mean, is the hypothesized population mean, and n is the sample size.

Than we find out the P-value. (By using calculator)

Interpret results.

If the P-value is greater than the significance level (0.05), we have to accept the null hypothesis.

If the P-value is less than the significance level (0.05), we have to reject the null hypothesis.

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