Question

1. A sample dataset with 25 values was randomly generated from a normally distributed random variable with a mean of 100.  The randomly selected data points are presented in the following table:

91	90	103	94	103
88	110	89	80	99
123	99	100	88	103
103	91	122	90	100
120	98	97	107	97

1. What kind of sample data do you have? Select the appropriate type of data
   1. One sample
   2. Paired sample
   3. Two samples
2. Based on what you know about the distribution of the data points, what is the preferred method of statistical analysis for the data?  Justify your answer
3. Can you use an alternative equivalent statistical test?  Justify your answer

I need help trying to explain and solve b and c!!

Answer 1

b) Since the sample is taken from Normal population with mean 100, the preferred method of statistical analysis for the data will be using z-test to test the hypothesis whether sample mean is 100 or not, i. e., H_o : mu = 100 versus H₁ : mu 100.

A z-test is any statistical test for which distribution of test statistic under null hypothesis can be approximated by normal distribution. Under null hypothesis, mu=100 hence the sample has same mean as of population. Therefore, using z test for statistical analysis of above data set will be preferred, based on the knowledge we have about the distribution of the data points.

C) Since sample size is small, ( < 30), and since the population standard deviation is unknown, we have to estimate the population standard deviation from the sample itself. Hence, using t-test will be precise for statistical analysis rather than z-test.

For performing the testing of hypothesis, i am using R software and attaching the image of code and output.

p-value of test (0.7843) is greater that of level of significance (0.05), hence we accept null hypothesis that sample mean is equal to population mean (=100) at 0.05 level of significance.

Hope this helped. All the best..!