Question

Test the claim that the population of sophomore college students has a mean grade point average greater than 2.25. Sample statistics include n = 51, xbar = 2.39, and s = 0.9. Use a significance level of significance= 0.05.

Question 1:

The test statistic is:

Question2:

The P-Value is between : ____< P-value < _____

Got t statistic is 1.1108 which is correct but am having trouble finding answer to second question. Please explain how to find it as well if you can

Answer 1

We want to test the claim that the population of sophomore college students has a mean grade point average greater than 2.25.

Therefore, the null and alternative hypotheses are,

H0 : μ = 2.25

Ha : μ > 2.25

This hypothesis test is a right-tailed test.

Test statistic = t = 1.111

Degrees of freedom = 51 - 1 = 50

In t-table, 50 is not given as degrees of freedom, so we can consider degrees of freedom of 40. In t-table we check test statistic = 1.111 is lies in which two values and corresponding their one-tail area is nothing but a range for a p-value given at the top of the t-table. Complete information shown in below image.

Therefore, we get, p-value is between : 0.100 < p-value < 0.150

Note : Using Excel we can find p-value as follows :

Excel Command : =TDIST (1.111, 50, 1) = 0.1359

=> p-value = 0.1359

0 cum. prob one-tail two-tails t.50 0.50 1.00 0.75 0.25 0.50 .80 0.20 0.40 4.85 0.15 0.30 0.90 0.10 0.20 0.95 0.05 0.10 0.975 0.025 0.05 t.99 0.01 0.02 .995 0.005 0.01 t.999 .9995 0.001 0.0005 0.002 0.001 636.62 31.599 12.924 8.610 14 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0% 1.000 0.816 0.765 0.741 0.727 0.718 0.711 0.706 0.703 0.700 0.697 0.695 0.694 0.692 0.691 0.690 0.689 0.688 0.688 0.687 0.686 0.686 0.685 0.685 0.684 0.684 0.684 0.683 0.683 0.683 0.681 0.679 0.678 0.677 0.675 0.674 50% 1.376 1.963 1.061 1.386 0.978 1.250 0.941 1.190 0.920 1.156 0.906 1.134 0.896 1.119 0.889 1.108 0.883 1.100 0.8791.093 0.876 1.088 0.873 1.083 0.870 1.079 0.868 1.076 0.866 1.074 0.865 1.071 0.863 1.069 0.862 1.067 0.861 1.066 0.860 1.064 0.859 1.063 0.858 1.061 0.858 1.060 0.857 1.059 0.856 1.058 0.856 1.058 0.855 1.057 0.855 1.056 0.854 1.055 0.854 1.055 0.851 1.050 0.848 1.045 0.846 1.043 0.845 1.042 0.842 1.037 0.842 1.036 60% 70% 3.078 6.314 12.71 1.886 2.920 4.303 1.638 2.353 3.182 1.533 2.132 2.776 1.476 2.015 2.571 1.440 1.943 2.447 1.415 1.895 2.365 1.397 1.860 2.306 1.383 1.833 2.262 1.372 1.812 2.228 1.363 1.796 2.201 1.356 1.782 2.179 1.350 1.771 2.160 1.345 1.761 2.145 1.341 1.753 2.131 1.337 1.746 2.120 1.333 1.740 2.110 1.330 1.734 2.101 1.328 1.729 2.093 1.325 1.725 2.086 1.323 1.721 2.080 1.321 1.717 2.074 1.319 1.714 2.069 1.318 1.711 2.064 1.316 1.708 2.060 1.315 1.706 2.056 1.314 1.703 2.052 1.313 1.701 2.048 1.311 1.699 2.045 1.310 1.697 2.042 1.303 1.684 2.021 1.296 1.671 2.000 1.292 1.664 1.990 1.290 1.660 1.984 1.282 1.646 1.962 1.282 1.645 1.960 80% 90% 95% Confidence Level 3 1.82 6.965 4.541 3.747 3.365 3.143 2.998 2.896 2.821 2.764 2.718 2.681 2.650 2.624 2.602 2.583 2.567 2.552 2.539 2.528 2.518 2.508 2.500 2.492 2.485 2.479 2.473 2.467 2.462 2.457 2.423 2.390 2.374 2.364 2.330 2.326 98% 63.66 9.925 5.841 4.604 4.032 3.707 3.499 3.355 3.250 3.169 3.106 3.055 3.012 2.977 2.947 2.921 2.898 2.878 2.861 2.845 2.831 2.819 2.807 2.797 2.787 2.779 2.771 2.763 2.756 2.750 2.704 2.660 2.639 2.626 2.581 2.576 99% 318.31 22.327 10.215 7.173 5.893 5.208 4.785 4.501 4.297 4.144 4.025 3.930 3.852 3.787 3.733 3.686 3.646 3.610 3.579 3.552 3.527 3.505 3.485 3.467 3.450 3.435 3.421 3.408 3.396 3.385 3.307 3.232 3.195 3.174 3.098 3.090 99.8% 5.959 5.408 5.041 4.781 4.587 4.437 4.318 4.221 4.140 4.073 4.015 3.965 3.922 3.883 3.850 3.819 3.792 3.768 3.745 3.725 3.707 3.690 3.674 3.659 3.646 3.551 3.460 3 .416 3.390 3.300 3.291 99.9% 801 1001 1000

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