I just need help with C-EIf its helpful for A) I got 21 degrees of freedom and B) I got [-1.721, 1.721] 7.20 A one-sample t test. The one-sample t statistic fortestingHo: μ = 8Ha: μ > 8from a sample of n = 22 observations has the valuet = 2.24.(a) What are the degrees of freedom for this statistic?(b) Give the two critical values t* from Table D thatbracket t.(c) Between what two values does the P-value of thetest fall?(d) Is the value t = 2.24 significant at the 5% level? Is itsignificant at the 1% level?(e) If you have software available, find the exact P-value.

The information provided in the question are as follows : The null and alternative hypotheses are given as, H0 : µ = 8 Ha : µ > 8 (right - tailed) (> represents right-tailed test) Degree of freedom = 21 Observed t-value = 2.24Part (c) : We know that, observed t-value = 2.24 And, degree of freedom = 21 Using t-distribution table (right - tailed), the observed value of t i.e., 2.24 for 21 degree of freedom lies between 2.080 and 2.518 there corresponding significance level are 0.025 and 0.01 respectively. Hence, the P-value of the observed t-value lies between 0.025 and 0.01. ANSWER : P-value lies between 0.01 and 0.025. Part (d) : The are two approaches to check the significance. P-value approach : If P-value < level of significance, then the results are statistically significant at given level of significance. If P-value > level of significance, then the results are not statistically significant at given level of significance. For level of significance = 5% or 0.05 : From the part (c) we know that the, P-value lies between 0.025 and 0.01, ⇒0.01 < P-value < 0.025 It can be easily seen that , P-value < 0.05. Hence, the results are statistically significant at 5% level. For level of significance = 1% or 0.01 : As we know that, 0.01 < P-value < 0.025. ⇒P-value > 0.01 Since, the P-value is greater the level of significance results are not statistically significant at 1% level. Critical value approach : For right-tailed test - If the observed t-value (to) is less than the critical value of t (tc) at given level of significance. We fail to reject the null and results are significant at given level of significance. If to is greater than tc at given level of significance. We reject the null hypothesis and results are not statistically significant at given level of significance. For level of significance 5% or 0.05 : The observed value of t (to) = 2.24 From the t-distribution table the critical value of t (tc) for 21 degree of freedom at 0.05 level of significance is 1.721 i.e, tc = 1.721, ⇒to > tc Hence, the results are statistically significant. For level of significance 1% or 0.01 : The observed value of t (to) = 2.24 From the t-distribution table the critical value of t (tc) for 21 degree of freedom at 0.05 level of significance is 2.518 i.e, tc = 2.518, ⇒to < tc Hence, the results are not statistically significant. Part (e) : As it is not possible to get the exact P-value using distribution table Therefore, using statistical software, the exact P-value is 0.01801848. The above P-value is calculated using the R function : pt(q, df, lower.tail=FALSE) Where, q = observed t-value, df = degree of freedom. And on providing, lower.tail = False gives the right-tailed value of t. ANSWER : The exact P-value = 0.01801848