The U.S. National Center for Health Statistics records information on each new baby born ...

The U.S. National Center for Health Statistics records information on each new baby born, such as time and date of births, weight, and sex.  On bit of information available from these data is the day of the week on which each baby was born.  Under the proportional model, we would expect that babies should be born at the same frequency on all seven days of the week.  But is this true?  The following table lists the number of babies born on each day of the week in a random sample of 350 births. 

Day

Number of   Births

Sunday

33

Monday

41

Tuesday

63

Wednesday

63

Thursday

47

Friday

56

Saturday

47

Write a null and alternative hypothesis to test the claim that the proportion of births should be 1/7 for each day of the week.

Test this hypothesis giving the test statistic and p-value and conclusion about this test.  (You can use R to get the values).