**Exercise 5: Hypothesis Testing Using T-Distribution**---**Context:**This exercise involves conducting hypothesis tests based on a random sample drawn from an approximately normal population with an unknown standard deviation. The task is to determine the p-value for each scenario described, and visually represent this by drawing a t-curve and shading the region corresponding to the p-value.**Instructions:**For each set of hypotheses, sample size, and T-statistic given below, follow these steps:1. Determine the p-value.2. Draw a t-distribution curve.3. Shade the region under the curve that corresponds to the p-value.Note: Since precise p-values cannot always be determined using t-tables, providing a range suffices.---**Scenarios:**(a) **Hypothesis:** \( H_A : \mu > 0.5 \) **Sample Size:** \( n = 26 \) **T-Statistic:** \( T = 2.6 \)(b) **Hypothesis:** \( H_A : \mu \neq 0.5 \) **Sample Size:** \( n = 26 \) **T-Statistic:** \( T = 2.6 \)(c) **Hypothesis:** \( H_A : \mu < 3 \) **Sample Size:** \( n = 18 \) **T-Statistic:** \( T = -2.2 \)(d) **Hypothesis:** \( H_A : \mu < 3 \) **Sample Size:** \( n = 18 \) **T-Statistic:** \( T = 2.2 \)---**Graphical Explanation:**For each scenario, the following should be depicted:1. **T-Curve:** - The curve is symmetrical around zero and represents the t-distribution specific to the degrees of freedom corresponding to each sample size.2. **Shaded Region:** - For a one-tailed test (as in cases (a) and (c)), shade the area in the direction of the alternative hypothesis. - For a two-tailed test (as in case (b)), shade both tails of the distribution. - The area shaded represents the probability related to the calculated T-statistic.---Using this setup, visually and analytically interpret each scenario to gain insight into the hypothesis testing framework using the t-distribution.

Since you have posted a question with multiple sub-parts, we will solve first three sub- parts for you. To get remaining sub-part solved please repost the complete question and mention the sub-parts to be solved (a) State the hypotheses. Obtain the degrees of freedom. From the information, given that n=26, T=2.6 The degrees of freedom is obtained below as follows: Use Excel to obtain the probability value. Follow the instruction to obtain the P-value: Open EXCEL Go to Formula bar. In formula bar enter the function as“=TDIST” Enter the test statistic as 2.60 Enter the degrees of freedom as 25 Enter the tails as 1. Click enter EXCEL output: From the Excel output, the P-value is 0.0077 Thus, the P-value is 0.0077 Sketch the area of curve with respect to the P-value. (b) State the hypotheses. From the information, given that n=26, T=2.6 Use Excel to obtain the probability value. Follow the instruction to obtain the P-value: Open EXCEL Go to Formula bar. In formula bar enter the function as“=TDIST” Enter the test statistic as 2.60 Enter the degrees of freedom as 25 Enter the tails as 1. Click enter EXCEL output: From the Excel output, the P-value is 0.0077 The P-value in two tail is 0.0154(=2*0.0077). Thus, the P-value is 0.0154 Sketch the area of curve with respect to the P-value. (c ) State the hypotheses. Obtain the degrees of freedom. From the information, given that n=18, T=–2.2 The degrees of freedom is obtained below as follows: Use Excel to obtain the probability value. Follow the instruction to obtain the P-value: Open EXCEL Go to Formula bar. In formula bar enter the function as“=TDIST” Enter the test statistic as ABS(–2.2) Enter the degrees of freedom as 17 Enter the tails as 1. Click enter EXCEL output: From the Excel output, the P-value is 0.0210 Thus, the P-value is 0.0210 Sketch the area of curve with respect to the P-value.