4 **t-Distribution Table***Area in Right Tail*This table provides critical values of the t-distribution for various significance levels in the right tail. The table is organized based on degrees of freedom (df), ranging from 1 to 1000. Critical t-values are provided for areas (probabilities) of 0.25, 0.20, 0.15, 0.10, 0.05, 0.025, 0.02, 0.01, 0.005, 0.0025, 0.001, 0.0005.- **Degrees of Freedom (df):** Located in the first and last columns, this ranges from 1 to 40, with select values continuing to 1000.- **Probability Levels:** Displayed at the top and bottom of the table, representing the area in the right tail of the t-distribution.For example, with 5 degrees of freedom and an area of 0.05 in the right tail, the critical t-value is 2.571.The values across the row represent increasing critical values as the confidence level becomes stricter (e.g., from 0.25 to 0.0005). As the degrees of freedom increase, the critical t-values generally decrease, reflecting the convergence to the normal distribution. **T-Test for a Sample Mean**To test \( H_0: \mu = 40 \) versus \( H_1: \mu < 40 \), a random sample of size \( n = 26 \) is obtained from a population that is known to be normally distributed. Complete parts (a) through (d) below.---**(a)** If \( \bar{x} = 37.2 \) and \( s = 14.9 \), compute the test statistic.\[ t_0 = -0.958 \] (Round to three decimal places as needed.)---**(b)** If the researcher decides to test this hypothesis at the \( \alpha = 0.1 \) level of significance, determine the critical value(s). Although technology or a t-distribution table can be used to find the critical value, in this problem use the t-distribution table given.Critical Value: \[ \_\_\_\_\_\_ \](Round to three decimal places. Use a comma to separate answers as needed.)

ɑ=0.10, n=26 tcrtitcal=? Hypothesis Ho: μ=40 vs H1: μ<40 (left tail) (b) tcritical= tɑ,n-1= -1.316

To test Ho: µ= 40 versus H4: µ< 40, a random sample of size n = 26 is obtained from a population that is known to be normally distributed. Complete parts (a) through (d) below. E Click here to view the t-Distribution Area in Right Tail. a) If x= 37.2 and s= 14.9, compute the test statistic. n = - .958 (Round to three decimal places as needed.) b) If the researcher decides to test this hypothesis at the a = 0.1 level of significance, determine the critical value(s). Although technology or a t-distribution table can be used to find the critical value, n this problem use the t-distribution table given. Critical Value: Round to three decimal places. Use a comma to separate answers as needed.)