Why is "at home" correct?

[Prepo]

English Grammar Tests, Elementary Level

ESL/EFL Test #111 "Postcard: Holiday", question 8

I do hope the weather ......... home is better than it is here.

(a) at
(b) in
(c) by

English Grammar Tests, Elementary Level

ESL/EFL Test #111 "Postcard: Holiday", answer 8

I do hope the weather at home is better than it is here.

Correct answer: (a) at

Your answer was: incorrect
I do hope the weather by home is better than it is here.
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i did say by

[Mister Micawber]

.
And 'by' is incorrect. The correct answer is written above.
.
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Native English teacher at Mister Micawber's

[Saneta]

What is the difference between :''I do hope the weather..'' and 'I hope the weather..''? Does ''do'' constitute the emphasis?? When should I use words do/does + verb in declarative sentences with Present Simple tense?? Thanks a lot

[Mister Micawber]

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Yes, it is used for emphasis.
.
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Native English teacher at Mister Micawber's