Question

Consider the following hypotheses:

H₀: μ ≤ 37.9
H_A: μ > 37.9

A sample of 31 observations yields a sample mean of 39.3. Assume that the sample is drawn from a normal population with a population standard deviation of 4.2. Tables provided below z table or t table****

a-1. Find the p-value.

• 0.05  p-value < 0.10
• p-value  0.10

• p-value < 0.01

• 0.01  p-value < 0.025
• 0.025  p-value < 0.05

a-2. What is the conclusion if α = 0.01?

• Reject H₀ since the p-value is greater than α.

• Reject H₀ since the p-value is smaller than α.

• Do not reject H₀ since the p-value is greater than α.

• Do not reject H₀ since the p-value is smaller than α.

a-3. Interpret the results at α = 0.01.

• We conclude that the sample mean is greater than 37.9.

• We cannot conclude that the sample mean is greater than 37.9.

• We conclude that the population mean is greater than 37.9.

• We cannot conclude that the population mean is greater than 37.9.

b-1. Calculate the p-value if the above sample mean was based on a sample of 110 observations.
  

• p-value < 0.01

• 0.01  p-value < 0.025
• 0.025  p-value < 0.05
• 0.05  p-value < 0.10
• p-value  0.10

b-2. What is the conclusion if α = 0.01?
  

• Reject H₀ since the p-value is smaller than α.

• Reject H₀ since the p-value is greater than α.

• Do not reject H₀ since the p-value is smaller than α.

• Do not reject H₀ since the p-value is greater than α.

b-3. Interpret the results at α = 0.01.

• We conclude that the sample mean is greater than 37.9.

• We cannot conclude that the sample mean is greater than 37.9.

• We conclude that the population mean is greater than 37.9.

• We cannot conclude that the population mean is greater than 37.9.

T table provided below***

| 0.20 1.376 1.061 0.978 0.941 0.920 0.906 0.896 0.889 0.883 0.879 0.10 3.078 1.886 1.638 1.533 1.476 1.440 1.415 1.397 1.383 1372 0.05 6.314 2.920 2.353 2.132 2.015 1.943 1.895 1.860 1.833 1.812 0.025 12.706 4.303 3.182 2.776 2.571 2.447 2.365 2.306 2262 2.228 31.821 6.965 4.541 3.747 3.365 3.143 2.998 2.896 2.821 2.764 0.005 63.657 9.925 5.841 4.604 4.032 3.707 3499 3.355 3.250 3.169 2.201 2.179 1.363 1.356 1.350 1.345 1.341 0.876 0.873 0.870 0.868 0.866 0.865 0.863 0.862 0.861 0.860 1796 1.782 1771 1.761 1753 1.746 1740 1.734 1729 1725 2.718 2.681 2.650 2.624 2.602 2.583 2567 2.552 2.539 2.528 2.160 2.145 2.131 2.120 2.110 2.101 2.093 2.086 3.106 3.055 3.012 2.977 2947 2921 2.898 2.878 2.861 2.845 1.337 1.333 1330 1.328 1325 0.859 0.858 0.858 0.857 0.856 0.856 0.855 0.855 0.854 0.854 1.323 1.321 1319 1.318 1316 1.315 1.314 1.313 1.311 1310 1721 1717 1.714 1.711 1.708 1.706 1.703 1701 1.699 1.697 2.080 2.074 2.069 2.064 2.060 2.056 2.052 2.048 2.045 2.042 2.518 2.508 2.500 2.492 2.485 2.479 2.473 2.467 2.462 2.457 2.831 2.819 2.807 2.797 2.787 2.779 2.771 2.763 2.756 2.750 0.853 0.853 0.853 0.852 0.852 0.852 0.851 0.851 0.851 0.851 1.309 1.309 1308 1.307 1.306 1.306 1.305 1.304 1.304 1.303 1.696 1.694 1.692 1.691 1.690 1.688 1.687 1.686 1.685 1.684 2.040 2.037 2.035 2.032 2.030 2.028 2.026 2024 2.023 2.021 2453 2.449 2.445 2.441 2.438 2434 2.431 2.429 2.426 2423 2.744 2.738 2.733 2.728 2.724 2.719 2.715 2.712 2.708 2.704

Z table provided below***

Answer 1

DATE ........ - perge-2 bli - given - test that .. Statistic nallo & z- 39.3-37.9 - 42 to - 1.9 0.40 | z= 3.50 / p.value & we know z=3.50 - it is right tail rest Pavalue pez7 8.50) Pavalue = 0.00 0 233 - P-value Loiol Ibra The Conclusion Pvalue a s 0.000 223 x 00) if if d = o.o. Reject Mo Reject Ho gince the p-value is smallee thana population mean b.3 we Conclude that the is greatee than 379