please show and explain step by step.

The owner of a business has based decisions on the average age of customers historically being 30 years. A random sample of customers' ages (in years) is shown below. Based on this sample, is the average age more than 30 years? Use a 10% level of significance. Assume that the distribution of ages is normal.

37 30 26 35 45 42 51

43 27 39 38 46 21 28

a. State the null and alternate hypotheses. Will you use a left-tailed, right-tailed, or two-tailed test?

b. What distribution do we use for the sample test statistic? Check the requirements for using this distribution.

c. Calculate the sample mean and standard deviation using EXCEL. (You do not need to submit your EXCEL workbook. Just use your results here.)

d. What is the value of the test statistic?

e. Determine the p-value. Sketch the distribution and shade the area corresponding to the p-value.

f. Will you reject or fail to reject the null hypothesis? Are the data statistically significant?

g. State your conclusion in the context of the application.