Researchers conducted a study to investigate the factors affecting the progression of pneumonia in novel coronavirus disease 2019 (COVID-19) patients who were admitted to three tertiary hospitals in Wuhan between December 30, 2019 and January 15, 2020. They collected individual data, laboratory indices, imaging characteristics, and clinical data, including albumin levels (g/L). Albumin is a protein produced by your liver that helps to keep fluid in your bloodstream, so it does not leak into other tissues. It also carries hormones, vitamins, and enzymes throughout your body. Low albumin levels can indicate a problem with your liver or kidneys. Based on clinical typing results, the patients were divided into a progression group (n=11) or an improvement/stabilization group (n=67). The mean albumin level in the progression group was 36.62 g/L with a standard deviation of 6.60 g/L. The mean albumin level in the improvement/stabilization group was 41.27 g/L with a standard deviation of 4.85 g/L. Using a 0.05 significance level, you need to test the claim that patients in the progression group had significantly lower albumin levels than patients in the improvement/stabilization group. To do so, assume the population variances are equal and answer each of the following questions.

1) what is the null hypothesis?

2)what is the alternative hypothesis?

3)what is the value of the test statistic you should use to test the given hypothesis?

4)if population variances are unequal, what value would you use for the denominator of the test statistic?

5) what is the p-value ( corresponding to test statistic in problem 3)

6) what conclusion should you make based on the data?