A dentist wondered if his appointments were distributed evenly from Monday to Friday each week. He took a random sample of 500 appointments and recorded which day of the week they were booked for. His results are: Appointment Frequency The dentist would like to use these results to conduct a x 2 goodness-offit test to determine if the distribution of appointments agrees with an even distribution using a 2.5% level of significance. Chi Square Distribution Table a. Calculate the test statistic. 3(2 = 0.00 E b. Determine the critical value(s) for the hypothesis test. +E c. Conclude whether to reject the null hypothesis or not based on the test statistic. O Reject O Fail to Reject A phone company plans on offering their new smartphone in four colours: white, black, silver and rose gold. They anticipate that 30% of shoppers will prefer white, 35% will prefer black, 20% will prefer silver and 15% will prefer rose gold. They perform market research by asking a random sample of 350 potential customers which colour they prefer. m- Can the company conclude that their expected distribution was accurate using a 5% level of significance? Chi Square Distribution Table ' a. Calculate the test statistic. 0.00 E b. Determine the critical value(s) for the hypothesis test. +E c. Conclude whether to reject the null hypothesis or not based on the test statistic. O Reject O Fail to Reject Use the Chi Square Distribution Table to find the following critical x 2 values. I Chi Square Distribution Table I Complete the following instructions: i. Identify the independent and dependent variables. ii. Calculate and interpret the Pearson correlation coefficient r for the paired data. Be sure to indicate ifthe correlation is positive or negative, and whether it is strong, moderate, or weak, or if there does not appear to be any significant correlation. An LCBO employee compares the relationship between the price of6 different vintage bottles of wine, and the number of those bottles that have been purchased in the last 3 months to see if there is a correlation between the number of bottles purchased and the price of the bottle. Number of Bottles of Wine Purchased in the Price of Wine Bottle ($) Last 3 Months Independent Variable: Dependent Variable: V Pearson Correlation Coefficient (r): 0.000 5 Round to 3 decimal places. Correlation: Correlation Strength: V I T-Distribution Table I a. Calculate the test statistic. t = 0.000 5 Round to three decimal places if necessary H1: p #0 r=0.11 n=273 0c=0.2 b. Determine the critical value(s) for the hypothesis test. +8 c. Conclude whether to reject the null hypothesis or not based on the test statistic. O Reject O Fail to Reject An online marketplace retailer performed a study that compared the average domestic shipping time of 99 sellers with their overall seller satisfaction rating (as a percent). The study yielded a sample correlation coefficient of r = -0.107. Test the claim that there is no linear correlation between the seller's average shipping time and their overall satisfaction rating at the 10% level of significance. T-Disti'i'butiori' Table a. Calculate the test statistic. t = 0.000 5 Round to three decimal places ffnecessaijy b. Determine the critical value(s) for the hypothesis test. +E c. Conclude whether to reject the null hypothesis or not based on the test statistic. O Reject O Fail to Reject A random sample of n1 = 19 securities in Economy A produced mean returns of x 1 = 5.6% with s1 = 2.1% while another random sample of n2 = 18 securities in Economy B produced mean returns of X 2 = 4.6% with s2 = 2.5%. At a = 0.2, can we infer that the returns differ significantly between the two economies? Assume that the samples are independent and randomly selected from normal populations with equal population variances ( 6 12 = 6 2). T-Distribution Table a. Calculate the test statistic. t= 0.000 Round to three decimal places if necessaryb. Determine the critical value(s) for the hypothesis test. +5 Round to three decimal places if necessary c. Conclude whether to reject the null hypothesis or not based on the test statistic. O Reject O Fail to Reject In a sample of 80 borrowers who borrowed less than $1,000 from an online instant lender, 19 repaid late while in a sample of 120 who borrowed over $1,000, 40 repaid late. Is there enough evidence to conclude that those who borrow less than $1,000 are less like likely to repay late? Test at or = 0.1. Standard Normal distribution Table ' a. Calculate the test statistic. Letp1 be the proportion for borrowers who borrowed less than $1,000 and p2 be those who borrowed over $1,000. 2 = 0.00 5 Round to two decimal places if necessary Enter 0 if normal approximation cannot be used b. Determine the critical value(s) for the hypothesis test. + Round to two decimal places if necessary Enter 0 if normal approximation cannot be used c. Conclude whether to reject the null hypothesis or not based on the test statistic. O Reject O Fail to Reject O Cannot Use Normal Approximation E