i need help in this problem and i need to identified if this is an example of t-test or proportions test?

Lab #5 Hypothesis Testing - Problem 1 A researcher claims that the average cost of all rnen's athletic shoes is less than $S. The remarcher records the price of 36 randomly selected athletic shoes (listed below}. 611' 45 Ill) Ill} T5 llIII.I Tl} 4C! 9D 65 ll 35 T5 BID T5 BID 9D 35 55 TI] 35 3 5 9|} 9|} BID 5t} BID 35 till TI} 35 95 6C! 55 95 TI} Using MINITAB, test at the 5% signicance level if the mean cost of all men's athletic shoes is less than $811 The population standard deviation is $19.21}. FllW-UP questions. Examining the test decision: a. Explain how you made your decision to \"reject Ho" or \"not reject Ho\". b. According to the result of the hypothesis test, is the researcher correct that the mean cost of all men's athletic shoes is less than $S? EXPLAIN. c. Would the result of this hypothesis test he considered due to chance variation or statistically signith change? Why? Examining p_ossible errors: d. What type of error (that is, Type I or Type II) has possibly occurred? 1Why? e. What is the probability this error has occurred? EXTRA credit (no partial credit}: 1'. Describe the error, in terms of the problem, that has possibly occurred