A random sample of 46 adult coyotes in a region of northern Minnesota showed the average age to be x- 2.03 years, with sample standard deviation s - 0.76 years. However, it is thought that the overall population mean age of coyotes is u- 1.75. Do the sample data indicate that coyotes in this region of northern Minnesota tend to live longer than the average of 1.75 years? Use a - 0.01.A USE SALT(a) What is the level of significance?State the null and alternate hypotheses.O Hg: H- 1.75 yr; H,: < 1.75 yrO H H> 1.75 yr; H- 1.75 yrOH,i - 1.75 yr; H, > 1.75 yrO H,: - 1.75 yr; H, ** 1.75 yrO Hg: < 1.75 yr; H,- 1.75 yr(b) What sampling distribution will you use? Explain the rationale for your choice of sampling distribution.O The Student's t, since the sample size is large and o is unknown.O The Student's t, since the sample size is large and o is known.O The standard normal, since the sample size is large and o is known.O The standard normal, since the sample size is large and o is unknown.What is the value of the sample test statistic? (Round your answer to three decimal places.)(c) Estimate the Pvalue.O Pvalue > 0.250O 0.100 < p.value < 0.250O 0.050 < P-value < 0.100O 0.010 < Pvalue < 0.050O P-value < 0.010Sketch the sampling distribution and show the area corresponding to the P-value.(d) Based on your answers in parts (a) to (C), wil you reject or fail to reject the nul hypothesis? Are the data statistically significant at level a?O At the a- 0.01 level, we reject the null hypothesis and conclude the data are statistically significant.O At the a- 0.01 level, we reject the null hypothesis and conclude the data are not statistically significant.O At the a - 0.01 level, we fail to reject the null hypothesis and condude the data are statistically significant.O At the a - 0.01 level, we fail to reject the null hypothesis and condude the data are not statistically significant.

The given sample size is 46, sample mean is 2.03, and sample standard deviation is 0.79. The population mean is 1.75.(a) The given alpha is 0.01. Therefore, the level of significance is 0.01. The claim is to check whether the coyotes in this region of northern Minnesota tend to live longer than the average of 1.75 years or not. The hypothesis is, Null hypothesis: H0:μ=1.75 yr Alternative hypothesis: H1:μ>1.75 yr(b) In this study the sample is large(which is greater than 30) and the population standard deviation is unknown indicating that the student's t distribution is appropriate to use. Therefore, the Student's t, since the sample size is large and σ is unknown. The value of the sample test statistic is, t=x¯-μsn=2.03-1.750.7646=0.280.1120558866777=2.49875≈2.499 Therefore, the value of the sample test statistic is 2.499.(c) The degrees of freedom is, df=n-1=46-1=45 The hypothesis is right tail. The probability of t greater than 2.49875 with 45 degrees of freedom can be obtained using the excel formula “=T.DIST.RT (2.49875, 45)”.The probability value is 0.0081 which is less than 0.010. Thus, the estimated P-value is < 0.010. The area corresponding to the P-value is,(d) Decision rule: If P-value≤α, then reject the null hypothesis. Conclusion: The P-value is less than the level of significance. Based on decision rule, reject the null hypothesis. Thus, the data are statistically significant. Correct Answer: Option 1.