**Title: Understanding Hypothesis Testing in Crime Rate Analysis**Is the national crime rate really going down? Some sociologists say yes! They attribute the decline in crime rates in the 1980s and 1990s to demographics, noting that an aging population may contribute to fewer crimes. According to the FBI and the Justice Department, 70% of all arrests are of males aged 15 to 34 years. Suppose you are a sociologist in Rock Springs, Wyoming, and a random sample of police files showed that of 36 arrests last month, 28 were of males aged 15 to 34 years. Use a 10% level of significance to test the claim that the population proportion of such arrests in Rock Springs is different from 70%.### Analysis:**(a) What is the level of significance?**Select the level of significance for this test.**State the null and alternate hypotheses.**1. \( H_0: p = 0.7, H_1: p > 0.7 \)2. \( H_0: p < 0.7, H_1: p = 0.7 \)3. \( H_0: p > 0.7, H_1: p = 0.7 \)4. \( H_0: p = 0.7, H_1: p \neq 0.7 \)5. \( H_0: p = 0.7, H_1: p < 0.7 \)**(b) What sampling distribution will you use?**Choose the appropriate sampling distribution:- The standard normal, since \( np > 5 \) and \( nq > 5 \).- The standard normal, since \( np < 5 \) and \( nq < 5 \).- The Student’s t, since \( np > 5 \) and \( nq > 5 \).- The Student’s t, since \( np < 5 \) and \( nq < 5 \).**What is the value of the sample test statistic?**(Round your answer to two decimal places.)**(c) Find the P-value of the test statistic.**(Round your answer to four decimal places.)**Sketch the sampling distribution and show the area corresponding to the P-value.****Graph Explanation:**The image contains two bell-shaped curves representing normal distributions. The shaded The text in the image is as follows:---- The Student’s t, since np > 5 and nq > 5.- The Student’s t, since np < 5 and nq < 5.**What is the value of the sample test statistic?** (Round your answer to two decimal places.)**(c) Find the P-value of the test statistic.** (Round your answer to four decimal places.)**Sketch the sampling distribution and show the area corresponding to the P-value.***Four diagrams of normal distribution curves are shown:*1. The first graph has a shaded area on the left tail.2. The second graph has shaded areas on both tails.3. The third graph has a shaded area in the left region close to the mean.4. The fourth graph has a shaded area on the right region close to the mean.**(d) Based on your answers in parts (a) to (c), will you reject or fail to reject the null hypothesis? Are the data statistically significant at level α?**- At the α = 0.10 level, we reject the null hypothesis and conclude the data are statistically significant.- At the α = 0.10 level, we reject the null hypothesis and conclude the data are not statistically significant.- At the α = 0.10 level, we fail to reject the null hypothesis and conclude the data are statistically significant.- At the α = 0.10 level, we fail to reject the null hypothesis and conclude the data are not statistically significant.**(e) Interpret your conclusion in the context of the application.**- There is sufficient evidence at the 0.10 level to conclude that the true proportion of arrests of males aged 15 to 34 in Rock Springs differs from 70%.- There is insufficient evidence at the 0.10 level to conclude that the true proportion of arrests of males aged 15 to 34 in Rock Springs differs from 70%.---

The question is about hypothesis testing.Given :Population proportion of arrests of males aged 15 to 34 years ( p ) = 0.70Randomly selected no. of arrests ( n ) = 36No. of arrests among " n " who were males aged 15 to 34 years ( x ) = 28To find :Test the claim that the population proportion of arrests is different from 70%.a )Significance level :Null and alternative hypothesis :Claim statement : The population proportion of arrests is different from 70%.The word "different " indicates ≠ sign, so it would go under alternative hypothesis.Hence,Answer : Option 4Uisng Salt,SALT -- > INFERENTIAL STATISTICSEnter the values under " Setting " part as follows and then click on " Generate Results ".b )Both values are greater than 5. Hence, the standard normal distribution need to be use.Answer : Option 1Sample test statistic :Z - statistic = 1.01835 ...from above salt outputRounding value to 2 decimal placesZ - statistic = 1.02c )P value = 0.308512 ....from above salt outputRounding value to 4 decimal places P value = 0.3085Graph :Shaded area indicates rejection region.Answer : Option 2d )Decision rule :i ) Reject H0 if ii ) Fail to reject H0 if Here, Hence, fail to reject H0So, the data are not statistically significant.Answer : Option 4e )Conclusion :There is insufficient evidence to conclude that the true proportion of arrests is different from 70%.Answer : Option 2a ) Significance level = 0.10Hypotheses :Answer : Option 4b )The standard normal, since and Answer : Option 1Sample test statistic = 1.02c )P value = 0.3085Graph :Answer : Option 2d ) Decision : Fail to reject H0. The data are nor statistically significant,Answer : Option 4e )Conclusion :There is insufficient evidence to conclude that the true proportion of arrests is different from 70%.Answer : Option 2