A report states that the mean number of texts that adults 18- to 24- years-old send and receive daily is 128. Suppose we take a sample of 25- to 34- year-olds to see if their mean number of daily texts differs from the mean for 18- to 24- year-olds.
(a)State the null and alternative hypotheses we should use to test whether the population mean daily number of texts for 25- to 34-year-olds differs from the population daily mean number of texts for 18- to 24-year-olds.
H0: μ [ Select ] ["less than", "less than or equal to", "equal to", "greater than", "greater than or equal to", "different from"] 128
Ha: μ [ Select ] ["less than or equal to", "greater than", "less than", "greater than or equal to", "equal to", "different from"] 128
(b) Suppose a sample of thirty 25- to 34-year-olds showed a sample mean of 118.2 texts per day. Assume a population standard deviation of 33.17 texts per day.
(c) What is the value of the test statistic? [ Select ] ["0.30", "-8.86", "-1.62", "8.86", "-0.30", "1.62"]
(d) State the critical values for the rejection rule, for an 𝛼 = 0.05.
Assume n=30 is large enough sample for the Central Limit Theorem to apply. If the test is one-sided, enter NONE for the unused tail.
Rejection rule: test statistic ≤ [ Select ] ["-2.58", "-1.28", "NONE", "-1.64", "-1.96", "-2.33"] or test statistic ≥ [ Select ] ["1.96", "1.28", "2.58", "2.33", "1.64", "NONE"]
(e) With 𝛼 = 0.05 as the level of significance, what is your conclusion? [ Select ] ["Reject H0. We cannot conclude that the population mean daily texts for 25-to-34-year-olds differs significantly from the mean for 18-24-year-olds.", "Do not reject H0. We can conclude that the population mean daily texts for 25-to-34-year-olds differs significantly from the mean for 18-24-year-olds.", "Do not reject H0. We cannot conclude that the population mean daily texts for 25-to-34-year-olds differs significantly from the mean for 18-24-year-olds", "Reject H0. We can conclude that the population mean daily texts for 25-to-34-year-olds differs significantly from the mean for 18-24-year-olds."]