11 A simple random sample of size n = 15 is drawn from a population that is normally distributed. The sample mean is found to be x = 23.2 and the sample standard deviation is found to be s = 6.3. Determine if the population mean is different from26 at the a = 0.01 level of significance. Complete parts (a) through (d) below......(a) Determine the null and alternative hypotheses.Ho:26H1:26(b) Calculate the P-value.P-value =(Round to three decimal places as needed.)(c) State the conclusion for the test.A. Reject Ho because the P-value is greater than the a = 0.01 level of significance.B. Reject Ho because the P-value is less than the a = 0.01 level of significance.O C. Do not reject H, because the P-value is less than the a = 0.01 level of significance.D. Do not reject H, because the P-value is greater than the a = 0.01 level of significance.

Given data : sample size, n = 15 sample mean, x̄ = 23.2 sample standard deviation,s= 6.3 population mean,μ= 26.0 Significance level, α= 0.01Solution : a) Hypothesis test : The null and alternative hypothesis is H0: u = 26.0 Ha: u ≠ 26.0B) Test statistic : =( 23.2 - 26.0 )/( 6.3 /V 15 ) = -1.72 The test statistic is -1.72 Degree of freedom df=n-1= 15 -1= 14 p - value P-value =2P(t>|tobs|) = 2 x P(t >| -1.72 |)= 0.107 ---------- (from student t - table) ∴ P-value= 0.107C) Do not reject Ho because the P-value is greater than the α = 0.01 level of significance. Answer - option D