lea knows the following information about the 50 days where she tracked whether she wore a tie and whether…

lea knows the following information about the 50 days where she tracked whether she wore a tie and whether she received a compliment on her outfit:\n\n. there were 11 days where she neither wore a tie nor received a compliment.\n\n. there were 30 days in total where she received a compliment.\n\n. there were 16 days in total where she did not wear a tie.\n\ncan you help lea organize the results into a two - way frequency table?\n\nwore a tie did not wear a tie\nreceived a compliment\ndid not receive a compliment

lea knows the following information about the 50 days where she tracked whether she wore a tie and whether she received a compliment on her outfit:\n\n. there were 11 days where she neither wore a tie nor received a compliment.\n\n. there were 30 days in total where she received a compliment.\n\n. there were 16 days in total where she did not wear a tie.\n\ncan you help lea organize the results into a two - way frequency table?\n\nwore a tie did not wear a tie\nreceived a compliment\ndid not receive a compliment

Answer

Explanation:

Step1: Calculate the number of days she did not receive a compliment

Total days (n = 50). Days she received a compliment (n_{compliment}=30). Using the formula (n_{no - compliment}=n - n_{compliment}) (n_{no - compliment}=50 - 30=20)

Step2: Calculate the number of days she did not wear a tie and did not receive a compliment

Given (n_{neither}=11) (days she neither wore a tie nor received a compliment). And (n_{did\ not\ wear\ tie}=16) Using the formula (n_{did\ not\ wear\ tie\ and\ no - compliment}=11)

Step3: Calculate the number of days she did not wear a tie and received a compliment

Using the formula (n_{did\ not\ wear\ tie\ and\ compliment}=n_{did\ not\ wear\ tie}-n_{did\ not\ wear\ tie\ and\ no - compliment}) (n_{did\ not\ wear\ tie\ and\ compliment}=16 - 11 = 5)

Step4: Calculate the number of days she wore a tie and received a compliment

Using the formula (n_{wore\ tie\ and\ compliment}=n_{compliment}-n_{did\ not\ wear\ tie\ and\ compliment}) (n_{wore\ tie\ and\ compliment}=30 - 5=25)

Step5: Calculate the number of days she wore a tie and did not receive a compliment

Using the formula (n_{wore\ tie\ and\ no - compliment}=n_{no - compliment}-n_{did\ not\ wear\ tie\ and\ no - compliment}) (n_{wore\ tie\ and\ no - compliment}=20 - 11 = 9)

Answer:

Wore a tie Did not wear a tie
Received a compliment 25
Did not receive a compliment 9