Question

1. When engaging in the weight control (fitness/fat burning) types of exercise, a person is expected to attain about 60% of their maximum heart rate. For 20-year-olds, this rate is approximately 120 bpm. A simple random sample of 30 persons of 20-year-olds was taken, and the sample mean was found to be 107 bpm with a sample standard deviation of 45 bpm. Researchers wonder if it is to conclude that the expected level is actually lower than 120 bpm. Assuming that the measurements represent a random sample from a normal population, Construct a 95% confidence interval for the population mean. Show work below.

Answer 1

Given :-

Sample size (n) = 30

Sample mean ($\bar X$) = 107 bpm

Sample standard deviation (Sx) = 45 bpm

Here using ti-83 calculator.

95% confidence interval for the population

mean is 90.197 to 123.8

TEXAS INSTRUMENTS TI-83 Plus TInterval (90.197,123.8) X=107 Sx 45 n=30 STAT PLOT F1 TBLSET F2 FORMAT F3 CALC F4 TABLE F5 Y= WINDOW ZOOM TRACE GRAPH QUIT INS MODE 2nd DEL A-LOCK LIST LINK ALPHA X,Т,Ө,п STAT TEST ANGLE B C DISTR DRAW МАТH VARS PRGM CLEAR APPS MATRIX D SIN-1 cOs-1 TAN-1 E G TC H x-1 SIN COS TAN J EE ) 7 x 2 P V 10x 7 LOG X L4 T L5 L6 V S W 4 5 6 LN RCL L1 Y L2 L3 МЕМ STO 1 2 3 + OFF CATALOG ANS ENTRY SOLVE i ON ENTER CO