A pharmaceutical brand has launched a new product for expectant mothers called "For-Mum Vitamin". The claimed benefit of this new product is to help increase the weight of new-born babies, which in turn is a factor in boosting the survival rate of babies.

The company collected data by taking a random sample of weights (in grams) for 44 new-born babies (born within a week) from a particular large zipcode. The sample was selected such that the mothers were taking the "For-Mum Vitamin". The company also gathered another random sample of weights (in grams) for 44 new-born babies (from the same zipcode during the same week) wherein the mothers were not taking the vitamin. The mothers in the two samples were otherwise comparable on all other aspects (except for moms taking vitamin versus not taking the vitamin).

The data can be found in the table below the questions below:

Show your calculations and logic - and USE EXCEL FORMULAS to solve the following problems where applicable.

(a) Using this data, generate a 90% confidence interval for the mean weight for babies (in grams) whose mom did take the Vitamin. Please report and interpret your estimated confidence interval.

(b)Answer the following questions after doing a hypothesis test to test the company's claim that the average increase in weight of babies for moms who take the vitamins compared to moms who do not take the vitamin is greater than 100 grams.

(i) Please write down the Null and alternate hypothesis for the test.

(ii) Please state the test that you used and report the t-Stat (t_calculated) and the t-cutoff(s) that you will be using from the test.

(iii) Based on the test please write down your conclusion, i.e. do you agree with the claim being made by the company?

Weight of new born babies (in grams)
Mom did not take Vitamin	Mom took Vitamin
3045	3673
3629	2053
3519	2952
1678	3864
3234	3748
2158	3863
3129	3476
1825	2234
3647	3940
2883	3963
1674	2129
3787	2770
1839	2776
3267	1564
3094	3090
1356	2470
1862	2879
1902	2027
2418	1947
1438	2243
3378	3252
2375	2556
3472	2184
3091	1680
1662	2661
2194	3559
3565	3200
1268	3183
2661	1679
3196	3936
2006	3232
2854	1952
1213	1530
2424	1807
3436	3083
1487	1639
1361	3946
2216	1950
1656	2218
2084	2549
3066	1459
3386	3370
3235	1899
2475	2647