September April73 7575 8257 5854 5665 7192 9256 5855 6053 52 The "Freshman 15" refers to the belief that college students gain 15 lb (or 6.8 kg) during their freshman year. Listed in the accompanyingtable are weights (kg) of randomly selected male college freshmen. The weights were measured in September and later in April. Use thelisted paired sample data, and assume that the samples are simple random samples and that the differences have a distribution that isapproximately normal. Complete parts (a) through (c).CHo: Hd ▼kgH₁: Hdkg(Type integers or decimals. Do not round.)Identify the test statistic.SeptemberApril73 75 57 54 65 92 56 55 5375 82 58 56 71 92 58 60 52a. 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, " 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?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 isthe significance level,the null hypothesis. Theresufficient 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 < d < 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 includesHoc. 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 isevidence to conclude that males gain weight during their freshman year. The confidence intervala weight gain of 6.8 kg.

Given that, The sample data is given as: September April 73 75 75 82 57 58 54 56 65 71 92 92 56 58 55 60 53 52a) The null hypothesis and the alternative hypothesis are given as: H0:μd=6.8 H1:μd>6.8 The t-test statistic is 2.92. The p-value is 0.0096. Since the p-value is less than the significance level, we reject the null hypothesis. 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 April. b) The confidence interval is calculated as: CL=d¯-tcritical×sdn,d¯+tcritical×sdn=2.6667-1.8595×2.73869,2.6667+1.8595×2.73869=0.9692,4.3642 The confidence interval is: 1.0 kg < μd < 4.4 kgBecause the confidence interval includes no 6.8. Thus, the confidence interval leads to the same conclusion reached in part (a). c) The test does not suggest the specific weight gain of 6.8 kg. But it does suggest that there is no evidence to conclude that males gain weight during their freshman year. The confidence interval does not include a weight gain of 6.8 kg.