PLEASE SHOW WORK

In a pulse rate research, a simple random sample of 500 men results in a mean of 80 beats per minute, and a standard deviation of 11.5 beats per minute. Based on the sample results, the researcher concludes that the pulse rates of men have a standard deviation less than 12 beats per minutes. Use a 0.05 significance level to test the researcher's claim.

(a) Identify the null hypothesis and alternative hypothesis.

(b) Determine the test statistic. Show all work; writing the correct test statistic.

(c) Determine the P-value for this test. Show all work; writing the correct P-value.

(d) Is there sufficient evidence to support the researcher's claim? Explain