6. Pepe, who is an old chihuahua in Taos, has a heart rate that seems to be faster than normal. According to the veterinary manual, the heart rate for chihuahuas has a normal distribution, with mean heart rate ofp =115 beats per minute, and population standard deviation 0 = 15. Over the past nine weeks, Pepe's heart rate in beats per minute measured: 120 130 114 133 122 125 124 117 128 The mean of this sample is i = 124. The vet will use hypothesis testing to examine the claim that Pepe's heart rate is faster than normal, using a level of significance of 5% a} To start the test, the vet states these facts: Ho: :1 = 115 H1: [1 > 115 a = 0.05 Explain the meaning of those three facts. 15 b} Next, the vet computes the standard error, SE = = 5. Then she sketches a normal curve, J6 marks the standard errors, and looks for the appropriate area for E > 124. Is this a right-tailed, left-tailed, or two-tailed test? How do you know? ___ f_....l l l l * ___ 100 105 110 115 120 125 130 c) Since a is known, the vet computes a z-score for the sample statistic, as shown below: x 124115 9 z = " = = E = 1.30 m. T Then the vet uses the normal distribution TABLE 5 to find the P-value. When she looks up 2 = 1.80, the corresponding probability is 0.9641. Then she calculates 1 0.9641 = 0.0359. Why did she subtract the table value from 1 to nd the P-value? d} Compare the P-value and the level of significance. Will you say \"reject\" or \"do not reject" the null hypothesis? Why? e) Based on this hypothesis testing, what is your conclusion about Pepe's heart rate