Why do alkyl groups have lower electronegativity versus hydrogen? How does this affect the acidity or alkalinity of alcohols?

At first glance, I think you were referring to hyperconjugation, and wondering about how #"C"-"H"# bonds can stabilize alkyl carbocations. It really isn't about electronegativity, but about the #p# orbital on the central C atom being vacant (and thus electropositive).

HYPERCONJUGATION OF CARBOCATIONS

In general, delocalized negative charge stabilizes a molecule.

Since the central #p# orbital (perpendicular to the molecular plane) of an alkyl carbocation is short on electron density, it is electropositive.

The alkyl #sigma# bonds can rotate, the #"C"-"H"# bonding-electron pairs can spread their (negative) electron density into the central carbon's (electropositive) #p# orbital.

Having more alkyl groups surrounding the central carbon thus stabilizes it more than having fewer.

(This is not, however, related to the electron-donating capability of alkyl groups. It is merely a result of removing a substituent and generating a positive charge, which generally makes the compound less stable anyways.)

ACIDITY OF ALKANES

Alkanes have a high #"pKa"#, on the order of #50~60# generally. That physically means it is difficult to deprotonate them. The equilibrium is basically like this:

#"RCH"_3# #larr# #"RCH"_2^(-) + "H"^(+)#

If one manages to deprotonate an alkane, then what would result is an exceptionally great (Lewis) base, whose electron density also happens to be extremely localized onto the frontal carbon atom, allowing for easy electron donation.

(Great nucleophilicity is the ability to gather electron density easily and donate it quickly, but great basicity is the thermodynamic instability of the compound in question.)

ACIDITY OF ALCOHOLS

Analogizing with alkanes, alcohols have hydroxyl groups (#-"OH"#), which are electron-donating as well, back onto the alkyl group's frontal carbon, since their #sigma# bonding molecular orbitals are doubly-occupied:

(The structural difference is that an oxygen atom is inserted between the terminal carbon's #"C"# and #"H"#, which alters the local environment of the #"H"# and brings us into a different context.)

That means the electron density is localized more in the #"C"-"O"# bond (towards #"O"#, since it is more electronegative than #"C"#) than the #"O"-"H"# bond. This weakens the #"O"-"H"# bond and makes that hydrogen acidic, instead of an alkyl hydrogen.

Therefore, alcohols are (much) more acidic than alkanes.

This is reflected in the #"pKa"# of alcohols being approximately #16#, and not #50~60#. Note that since this is a #log# scale, actually, alcohols are about #10^34# times more capable of singly-ionizing than alkanes.