Hi, I’m a beginner knitter. The person I’m knitting this hat for has an average size head, so, I followed the pattern as is. After a few rounds, it looked quite small to me so I measured the circumference and it was only 14”. I took it apart & did a swatch of ribbing. I used the same yarn & needles two sizes bigger(3.75mm). My gauge for ribbing with worsted yarn is 6 sts/inch. The pattern’s gauge is 14 sts/ 4 inches. The cast on sts are only 72 sts. To match the gauge, even with bigger needles than the pattern, I would need over 130 cast on sts.
From the photo, the yarn looks thicker than the yarn suggested in the pattern but I’m not sure. What needle size & yarn weight would you suggest? I don’t want to drastically change the look of the pattern. Please chime in & let me know. I really love this hat and want to knit it soon. I appreciate all your help. Thank you. 
Hello
Where did you get the pattern from? Do you have a link to it?
The yarn suggested has a suggested needle size of 5mm and gauge of 18st per 4", which could give 16 st per 4" in a rib pattern as rib pulls in (and stretches back out).
The pattern picture doesn’t look like it’s worked on anything as small as 3.25mm.
What is the name of the yarn you’re using?
What needle size is suggested on the ball band of your yarn?
You could try bigger needles, perhaps a 5mm for the rib, but depending on your yarn this might give a fabric which is too open to give the result you want. Worth a try though.
Depending where the pattern came from, there’s a chance someone mistranslated the needle size. A size 3 UK is 6.5mm which is bigger than suggested on the yarn info but some people like a more open knit fabric.
The cast on number is correct for the design of the pattern, there are 9 petals and 8 rib stitches for each section. To get the same design youd need yarn and needles that work to this number.
Where did you find the pattern? Can you give us the name of the site or a URL?
It does look like heavier than worsted weight or maybe worsed weight held double? More like a bulky weight despite the description of the yarn as #4 and requiring 137 yards (typical for ww). Size 3 needles are also very small even for worsted weight yarn so I’m wondering about the pattern source.
Hi, thank you so much for helping me. The yarn is just standard worsted weight(4). I don’t remember the brand. I bought it awhile ago and no longer have the orig. packaging. I also have chunky yarn(5) available and all the needle sizes. Can you tell the approximate yarn & needle size from the video? I appreciate any help you can provide. Thanks again. Have an amazing day. 
Here is the link to the written pattern.
There is also a video on Youtube but she began with saying cast on 72 sts and started the tutorial.
Hi, thank you so much for helping me. The yarn is just standard worsted weight(4). I don’t remember the brand. I bought it awhile ago and no longer have the orig. packaging. I also have chunky yarn(5) available and all the needle sizes. Can you tell the approximate yarn & needle size from the video? I appreciate any help you can provide. Thanks again. Have an amazing day.
Here is the link to the written pattern.
Knit hat pattern | interunet
There is also a video on Youtube but she began with saying cast on 72 sts and started the tutorial.
Essentially, you’d be redesigning this hat. You can play around with needle size and stitch number but as a beginner knitter, it might be best to find a good pattern and do that first. Make a hat or two and then design your own. You’ll have a better feel for the elements that go into the pattern including stitch number, yarn weight, repeat and stitch multiples.
A search on Ravelry (free to join) for a bulky hat or bulky, slouchy hat turns up pages of patterns, some free, some paid. You can see how other knitters have evaluated the patterns and see pattern errors noted (if any).
You could try some swatches with the yarns you have if you don’t know the brand or weight of yarn you may need to try several swatches on different size needles to see what the fabric is like.
Maybe try 5mm and see what you get, then try 6mm and compare the fabric in stockinnete and ribbing.
You might try the chunky yarn on some larger needles and see what gauge and fabric you get.
There is no limit to how many swatches you can work before setting out on the final hat.
Although it might sound like a waste of time swatches are really helpful and it’s all knitting practice. Then you might be able to follow the video or choose a different pattern more suitable to the yarn you have available.