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Although the sample size was only 25 (a value less than 40), we can still assume that the sampling distribution of the sample mean (i.e. the distribution of all possible sample means xs ) approximately follows a tdistribution with mean xμμ=and standard deviation xσapproximated by the standard error xsSEn=since: (1) the sample of credit card holders was randomly selected, (2) it is reasonable to assume that the amount charged by one of the 25 people sample doesn’t influence the amount charged by any other of these 25 people, (3) ()()1010 25250nN==≤≈hundreds of thousands, if not millions, since Nrepresents the total number of credit holders, and (4) we’re told that the variable’s values in the sample have a distribution that is nearly bell-shaped, with no outliers. Thus, using the TI calculator’s T-Test function with 00:1500Hμ≤&, 25n=, 1756x=, 843s=()0value175615000.07PP xμ⇒−=≥=≈, which is greater than 0.05α=. Answer:There is not sufficient evidence at the 0.05 level of significance to conclude that the mean amount charged by all credit card holders was greater than $1500. Of course, with this decision we could be making the correct decision or we could be making a Type II error. The population is all credit card holders & the parameter is the mean amount, μ, they charged in the past 12 months. The sample consists of the 25 credit card holders that were randomly selected and the statistic is the mean amount, x,they charged in the past 12 months. The variable (a quantitative variable) is the amount (in $) charged by credit card holders in the past 12 months. 38.The figure provided is the distribution of ages of forty participants in a special education program. Note that the participants’ ages were recorded in whole years. Use the information in this figure to answer the questions in parts (a) – (d) below. Include units of measurement with each value. (a)Describe the shape of this distribution. Answer: The distribution of ages is skewed to the rightor skewed right.
(b)Determine the mode age of the participants. The mode age is that age which occurred most frequently. From the histogram, we see that 50% of the 40 participants were 8 years old, 30% were 9 years old, 10% were 10 years old, and 10% were 11 years old. Thus, the age which occurred the most often was 8 years. (Since this is a statistic, we should report it to one more decimal place than the data was recorded.) Answer:The mode age of the participants is 8.0 years. (c)Determine the median age of the participants. The median age is the value such 50% of the all the ages in the sample are less than or equal to it and 50% of the ages in the sample are greater than or equal to it. Thus, from the discussion in part (b), the median age is 8.5 years. Answer:The median age of the participants is 8.5 years. (d)Determine the mean age of the participants.