It is claimed that the proportion of adults who use a mobile fitness app is 0.19. Believing a different proportion of adults use a mobile fitness app, a researcher surveys a random sample of 260 adults and finds the sample proportion who use a mobile fitness app to be 0.25. Use this information to conduct a hypothesis test at a significance (or alpha) level of 0.05.

10. What will the hypotheses be?

Ho: Ha:

11. What is the test statistic? Please calculate this value below.

12. What is the P-value?

13. Given the P-value you determined to answer Question 12, should you reject or fail to reject the null hypothesis? Please explain

14. Are the results of this hypothesis test statistically significant? Please explain why or why not.

Go back now to the hypothesis testing app: https://istats.shinyapps.io/Inference_prop/

Remember, for "Type of Inference," to select Significance Test. In the upper left corner, where it says "Enter Data," use the dropdown menu to select Number of Successes. In our mobile fitness app example, we have a sample size of 260, and the number of successes (to give us a sample proportion of 0.25) would need to be 65. Once you type in these numbers, be sure to type in the appropriate "Null Value" (i.e., the value of p), and select the appropriate direction for the Alternative hypothesis.

15. Does the P-value you got with the app match the P-value you obtained from Table B in order to answer Question 12? Please explain.

16. Below we have shared six different hypothesis testing scenarios. For each scenario, you are given the null and alternative hypotheses, along with the resulting test statistic. Use this information, along with Table B, to find the P-value for each scenario. Write or type that P-value below each scenario.

A. Ho: p = 0.75 vs. Ha: p

B. Ho: p = 0.25 vs. Ha: p ? 0.25, z = 1.7

C. Ho: p = 0.3 vs. Ha: p > 0.3, z = 1.7

d. Ho: p = 0.5 vs. Ha: p > 0.5, z = 2.2

e. Ho: p = 0.43 vs. Ha: p

f. Ho: p = 0.5 vs. Ha: p ? 0.5, z = -2.2

This is table B

4210123 TABLE B Percentile; of the Normal distributions Standard Standard Standard score Percentile score Percentile score Percentile 3.4 0.03 1.1 13.57 1.2 88.49 3.3 0.05 1.0 15.87 1.3 90.32 3.2 0.07 0.9 18.41 1.4 91.92 -3.1 0.10 -0.8 21.19 1.5 93.32 -3.0 0.13 -0.7 24.20 1.6 94.52 -2.9 0.19 -0.6 27.42 1.7 95.54 2.8 0.26 0.5 30.85 1.8 96.41 2.7 0.35 0.4 34.46 1.9 97.13 2.6 0.47 0.3 38.21 2.0 97.73 2.5 0.62 0.2 42.07 2.1 98.21 2.4 0.82 0.1 46.02 2.2 98.61 2.3 1.07 0.0 50.00 2.3 98.93 2.2 1.39 0.1 53.98 2.4 99.18 2.1 1.79 0.2 57.93 2.5 99.38 2.0 2.27 0.3 61.79 2.6 99.53 1.9 2.87 0.4 65.54 2.7 99.65 - 1.8 3.59 0.5 69.15 2.8 99.74 - 1.7 4.46 0.6 72.58 2.9 99.81 - 1.6 5.48 0.7 75.80 3.0 99.87 1.5 6.68 0.8 78.81 3.1 99.90 1.4 8.08 0.9 81.59 3.2 99.93 1.3 9.68 1.0 84.13 3.3 99.95 1.2 11.51 1.1 86.43 3.4 99.97