7:11 4A nutrition lab tested 40 hot dogs to see if their mean sodium content was less than the 325-mg upper limit set byregulations for "reduced sodium" franks. The mean sodium content for the sample was 321.5 mg with a standarddeviation of 19 mg. Assume that the assumptions and conditions for the test are met.a) Test the hypothesis that the mean sodium content meets the regulation.b) Will a larger sample size ensure that the regulations are met?a) Write appropriate hypotheses.Hoi H=325HA: H<325The test statistic is t= - 1.17.(Round to two decimal places as needed.)The P-value is(Round to three decimal places as needed.)<AAmylab.pearson.com..llLTE8

a) Suppose μ is the population mean sodium content.It is needed to test, whether the sodium content was less than the 325-mg. The null and alternative hypotheses are, Null hypothesis: H0: μ = 325. Alternative hypothesis: HA: μ < 325. The test is left tailed. In this case, the sample size is large enough (> 30). The population standard deviation is not given. The assumptions and conditions for the test are met. Hence, one sample t test will be used. The sample size is n = 40. The sample mean is, x̅ = 321.5. The sample standard deviation is s = 19. The test statistic is, t = (x̅ – μ) / (s/√n). = (321.5 – 325) / (19/√40) = –3.5/3.004163777 ≈ –1.17 The test statistic is –1.17. The degrees of freedom is, df = n – 1 = 40 – 1 = 39. Now, using the EXCEL formula =T.DIST(-1.17,39,TRUE) the P-value is obtained as approximately 0.125. The excel output is, Decision rule: If P-value is less than or equal to the level of significance, reject the null hypothesis. Otherwise fail to reject the null hypothesis. Assume that the level of significance is α = 0.05. Conclusion: The P-value of 0.125 is greater than α = 0.05. Fail to reject H0. There is not enough evidence to conclude that the sodium content was less than the upper limit of 325-mg, at 5% level of significance. b) There is inverse relation between the sample size and the standard error. In this case, the sample mean is less than the given limit. If the sample size increases, the standard error will decrease. As a result of that the P-value decreases. The smaller P-value indicates the rejection of null hypothesis. Thus, yes, a larger sample size ensure that the regulations are met,