in MVC CheckboxFor, how change selection by Javascript?

Question

I wrote this in MVC view:

<td>
    @Html.CheckBoxFor(modelItem => Model.Selected[5])
</td>

It generates:

<td>
    <div class="checker" id="uniform-Selected_5_">
        <span class="checked">
            <input id="Selected_5_" name="Selected[5]" type="checkbox" value="true">
        </span>
    </div>
    <input name="Selected[5]" type="hidden" value="false">
</td>

When a user clicks on the checkbox, the span value changes, but not checkbox value.

With the Javascript below, I change the value of the checkbox, but the span value doesn't change.

var name = "Selected_5_";
document.getElementById(name).checked = 1;