8.7 The "Freshman 15" refers to the belief that college students gain 15 lb (or 6.8 kg) during their freshman year. Listed in the accompanying table are weights (kg) of randomly selected male college freshmen. The weights were measured in September and later in April. Use the listed paired sample data, and assume that the samples are simple random samples and that the differences have a distribution that is approximately normal. Complete parts (a) through (c).| September | 54 | 55 | 66 | 72 | 58 | 57 | 52 | 57 | 59 ||-----------|----|----|----|----|----|----|----|----|----|| April | 56 | 58 | 71 | 59 | 56 | 58 | 53 | 59 | 62 |---**a.** Use a 0.05 significance level to test the claim that for the population of freshman male college students, the weights in September are less than the weights in the following April.In this example, μₓ is the mean value of the differences d for the population of all pairs of data, where each individual difference d is defined as the April weight minus the September weight. What are the null and alternative hypotheses for the hypothesis test?\[ H_0: \mu_d = 0 \text{ kg} \]\[ H_1: \mu_d > 0 \text{ kg} \](Type integers or decimals. Do not round.) **Identify the Test Statistic:**- **t = ☐** (Round to two decimal places as needed.)**Identify the P-Value:**- **P-value = ☐** (Round to three decimal places as needed.)**What is the Conclusion Based on the Hypothesis Test?**Since the P-value is **☐** the significance level, **☐** the null hypothesis. There **☐** sufficient evidence to support the claim that for the population of freshman male college students, the weights in September are less than the weights in the following April.**b. Construct the Confidence Interval that Could Be Used for the Hypothesis Test Described in Part (a):**- What feature of the confidence interval leads to the same conclusion reached in part (a)? - The confidence interval is **[☐ kg, ☐ kg].** (Type integers or decimals rounded to one decimal place as needed.)- What feature of the confidence interval leads to the same conclusion reached in part (a)? - Because the confidence interval includes **☐**, **☐** H₀.**c. What Do You Conclude About the Freshman 15 Belief?**The test does not address the specific weight gain of 15 lb, but it does suggest that there is **☐** evidence to conclude that males gain weight during their freshman year. The confidence interval **☐** a weight gain of 6.8 kg.

identify the test statistic - (Round to two decimal places as needed.) identify the P-value P-value (Round to three decimal places as needed.) What is the conclusion based on the hypothesis test? Since the P-value is the significance level, the null hypothesis. There b. Construct the confidence interval that could be used for the hypothesis test described in part (a). What feature of the confidence interval leads to the same conclusion reached in part (a)? The confidence interval is kg<< kg. (Type integers or decimals rounded to one decimal place as needed.) What feature of the confidence interval leads to the same conclusion reached in part (a)? Because the confidence interval includes ▼ H₂ c. What do you conclude about the Freshman 15 belief? The test does not address the specific weight gain of 15 lb, but it does suggest that there is sufficient evidence to support the claim that for the population of freshman male college students, the weights in September are less than the weights in the following Aprill evidence to conclude that males gain weight during their freshman year. The confidence interval a weight gain of 6.8 kg