Correct

大伙儿 vs 大家

/ dàhuǒr vs dàjiā /
Strokes

Definition

大伙儿 vs 大家 both are Pronouns, which means [all; everybody], (within a certain space or time).

Example

大伙儿 and 大家, both indicate the speaker may or may not be included, and 大伙儿 is more colloquial.
Example ① indicates a certain time in history and example ② indicates all of the people in the room who attend the banquet.

Of course, time and space cannot be separated,e.g. example ① indicates "a certain place in China" and example ② indicates "a certain space in a certain time".
1
shíhòu
时候
jiā
大家
  
(
huǒr  
大伙儿
  
)
dōu
méi
jiàn
guò
Ōuzhōu
欧洲
rén
  

Nobody had seen a European at that time. (certain time)

2
jiā
大家
  
(
huǒr  
大伙儿
  
)
zuò
入座
  
!

Let's take our seats. (certain space)

3
lái
bàogào
报告
jiā
大家
  
(
huǒr  
大伙儿
  
)
hǎo
xiāoxi
消息
  

Allow me to tell you a piece of good news. (The speaker is not included.)

4
Zánmen
咱们
jiā
大家
  
(
huǒr  
大伙儿
  
)
kuàir  
块儿
  

Let's go together. (The speaker is included.)

大家 can be used at very formal occasions or in official titles; 大伙儿 is not often used at very formal occasions because it is too colloquial.
Since example ⑤ indicates an official occasion, so 大伙儿 cannot be used.
5
jiā
大家
起立
  
,
chàng
guó
国歌
  

All stand up and sing the national anthem in chorus.

6
wàng
希望
jiā
大家
  
(
huǒr  
大伙儿
  
)
dōu
lái
cānjiā
参加
men
我们
de
  
大家
jiā
tán  
节目
jié

I hope all of you come to join our programme "Talks for All".